Novel Approaches to Numerical Software with Result Verification
Identifieur interne : 001677 ( Istex/Corpus ); précédent : 001676; suivant : 001678Novel Approaches to Numerical Software with Result Verification
Auteurs : Laurent Granvilliers ; Vladik Kreinovich ; Norbert MüllerSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2004.
Abstract
Abstract: Traditional design of numerical software with result verification is based on the assumption that we know the algorithm f(x 1,...,x n ) that transforms inputs x 1,...,x n into the output y=f(x 1,...,x n ), and we know the intervals of possible values of the inputs. Many real-life problems go beyond this paradigm. In some cases, we do not have an algorithm f, we only know some relation (constraints) between x i and y. In other cases, in addition to knowing the intervals x i , we may know some relations between x i ; we may have some information about the probabilities of different values of x i , and we may know the exact values of some of the inputs (e.g., we may know that x 1 = π/2). In this paper, we describe the approaches for solving these real-life problems. In Section 2, we describe interval consistency techniques related to handling constraints; in Section 3, we describe techniques that take probabilistic information into consideration, and in Section 4, we overview techniques for processing exact real numbers.
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DOI: 10.1007/978-3-540-24738-8_17
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Novel Approaches to Numerical Software with Result Verification</title><author><name sortKey="Granvilliers, Laurent" sort="Granvilliers, Laurent" uniqKey="Granvilliers L" first="Laurent" last="Granvilliers">Laurent Granvilliers</name><affiliation><mods:affiliation>IRIN, Université de Nantes, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: granvilliers@irin.univ-nantes.fr</mods:affiliation></affiliation></author><author><name sortKey="Kreinovich, Vladik" sort="Kreinovich, Vladik" uniqKey="Kreinovich V" first="Vladik" last="Kreinovich">Vladik Kreinovich</name><affiliation><mods:affiliation>Department of Computer Science, University of Texas at El Paso, 79968, El Paso, TX, USA</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: vladik@cs.utep.edu</mods:affiliation></affiliation></author><author><name sortKey="Muller, Norbert" sort="Muller, Norbert" uniqKey="Muller N" first="Norbert" last="Müller">Norbert Müller</name><affiliation><mods:affiliation>Abteilung Informatik, Universität Trier, 54286, Trier, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: mueller@uni-trier.de</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:54E3EE5AE7FA9EAB35FD40CC7300C9AF1867217F</idno><date when="2004" year="2004">2004</date><idno type="doi">10.1007/978-3-540-24738-8_17</idno><idno type="url">https://api.istex.fr/document/54E3EE5AE7FA9EAB35FD40CC7300C9AF1867217F/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001677</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001677</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Novel Approaches to Numerical Software with Result Verification</title><author><name sortKey="Granvilliers, Laurent" sort="Granvilliers, Laurent" uniqKey="Granvilliers L" first="Laurent" last="Granvilliers">Laurent Granvilliers</name><affiliation><mods:affiliation>IRIN, Université de Nantes, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: granvilliers@irin.univ-nantes.fr</mods:affiliation></affiliation></author><author><name sortKey="Kreinovich, Vladik" sort="Kreinovich, Vladik" uniqKey="Kreinovich V" first="Vladik" last="Kreinovich">Vladik Kreinovich</name><affiliation><mods:affiliation>Department of Computer Science, University of Texas at El Paso, 79968, El Paso, TX, USA</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: vladik@cs.utep.edu</mods:affiliation></affiliation></author><author><name sortKey="Muller, Norbert" sort="Muller, Norbert" uniqKey="Muller N" first="Norbert" last="Müller">Norbert Müller</name><affiliation><mods:affiliation>Abteilung Informatik, Universität Trier, 54286, Trier, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: mueller@uni-trier.de</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><imprint><date>2004</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">54E3EE5AE7FA9EAB35FD40CC7300C9AF1867217F</idno><idno type="DOI">10.1007/978-3-540-24738-8_17</idno><idno type="ChapterID">17</idno><idno type="ChapterID">Chap17</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Traditional design of numerical software with result verification is based on the assumption that we know the algorithm f(x 1,...,x n ) that transforms inputs x 1,...,x n into the output y=f(x 1,...,x n ), and we know the intervals of possible values of the inputs. Many real-life problems go beyond this paradigm. In some cases, we do not have an algorithm f, we only know some relation (constraints) between x i and y. In other cases, in addition to knowing the intervals x i , we may know some relations between x i ; we may have some information about the probabilities of different values of x i , and we may know the exact values of some of the inputs (e.g., we may know that x 1 = π/2). In this paper, we describe the approaches for solving these real-life problems. In Section 2, we describe interval consistency techniques related to handling constraints; in Section 3, we describe techniques that take probabilistic information into consideration, and in Section 4, we overview techniques for processing exact real numbers.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Laurent Granvilliers</name><affiliations><json:string>IRIN, Université de Nantes, France</json:string><json:string>E-mail: granvilliers@irin.univ-nantes.fr</json:string></affiliations></json:item><json:item><name>Vladik Kreinovich</name><affiliations><json:string>Department of Computer Science, University of Texas at El Paso, 79968, El Paso, TX, USA</json:string><json:string>E-mail: vladik@cs.utep.edu</json:string></affiliations></json:item><json:item><name>Norbert Müller</name><affiliations><json:string>Abteilung Informatik, Universität Trier, 54286, Trier, Germany</json:string><json:string>E-mail: mueller@uni-trier.de</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: Traditional design of numerical software with result verification is based on the assumption that we know the algorithm f(x 1,...,x n ) that transforms inputs x 1,...,x n into the output y=f(x 1,...,x n ), and we know the intervals of possible values of the inputs. Many real-life problems go beyond this paradigm. In some cases, we do not have an algorithm f, we only know some relation (constraints) between x i and y. In other cases, in addition to knowing the intervals x i , we may know some relations between x i ; we may have some information about the probabilities of different values of x i , and we may know the exact values of some of the inputs (e.g., we may know that x 1 = π/2). In this paper, we describe the approaches for solving these real-life problems. In Section 2, we describe interval consistency techniques related to handling constraints; in Section 3, we describe techniques that take probabilistic information into consideration, and in Section 4, we overview techniques for processing exact real numbers.</abstract><qualityIndicators><score>7.136</score><pdfVersion>1.3</pdfVersion><pdfPageSize>430 x 660 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>1043</abstractCharCount><pdfWordCount>13689</pdfWordCount><pdfCharCount>68687</pdfCharCount><pdfPageCount>32</pdfPageCount><abstractWordCount>178</abstractWordCount></qualityIndicators><title>Novel Approaches to Numerical Software with Result Verification</title><chapterId><json:string>17</json:string><json:string>Chap17</json:string></chapterId><refBibs><json:item><author><json:item><name>O Aberth</name></json:item></author><host><author></author><title>Precise Numerical Methods Using C++</title><publicationDate>1998</publicationDate></host><publicationDate>1998</publicationDate></json:item><json:item><author><json:item><name>K,R Apt</name></json:item></author><host><volume>22</volume><pages><last>1036</last><first>1002</first></pages><issue>6</issue><author></author><title>ACM Transactions on Programming Languages and Systems</title><publicationDate>2000</publicationDate></host><title>The Role of Commutativity in Constraint Propagation Algorithms</title><publicationDate>2000</publicationDate></json:item><json:item><author><json:item><name>F Benhamou</name></json:item><json:item><name>F Goualard</name></json:item></author><host><pages><last>82</last><first>67</first></pages><author></author><title>Proceedings of of CP'2000, Principles and Practice of Constraint Programming</title><publicationDate>2000</publicationDate></host><title>Universally Quantified Interval Constraints</title><publicationDate>2000</publicationDate></json:item><json:item><author><json:item><name>F Benhamou</name></json:item><json:item><name>F Goualard</name></json:item><json:item><name>L Granvilliers</name></json:item><json:item><name>J.-F Puget</name></json:item></author><host><pages><last>244</last><first>230</first></pages><author></author><title>Proceedings of ICLP'99, International Conference on Logic Programming</title><publicationDate>1999</publicationDate></host><title>Revising Hull and Box Consistency</title><publicationDate>1999</publicationDate></json:item><json:item><author><json:item><name>F Benhamou</name></json:item><json:item><name>D Mcallester</name></json:item><json:item><name>Van Hentenryck</name></json:item><json:item><name>P </name></json:item></author><host><pages><last>138</last><first>124</first></pages><author></author><title>Proceedings of ILPS'94, International Logic Programming Symposium</title><publicationDate>1994</publicationDate></host><title>CLP(Intervals) Revisited</title><publicationDate>1994</publicationDate></json:item><json:item><author><json:item><name>F Benhamou</name></json:item><json:item><name>W,J Older</name></json:item></author><host><volume>32</volume><pages><last>24</last><first>1</first></pages><issue>1</issue><author></author><title>Journal of Logic Programming</title><publicationDate>1997</publicationDate></host><title>Applying Interval Arithmetic to Real, Integer and Boolean Constraints</title><publicationDate>1997</publicationDate></json:item><json:item><author><json:item><name>J Blanck</name></json:item></author><host><volume>2064</volume><pages><last>394</last><first>389</first></pages><author></author><title>Springer Lecture Notes in Computer Science</title><publicationDate>2001</publicationDate></host><title>Exact Real Arithmetic Systems: Results of Competition</title><publicationDate>2001</publicationDate></json:item><json:item><author><json:item><name>C Bliek</name></json:item><json:item><name>B Neveu</name></json:item><json:item><name>G Trombettoni</name></json:item></author><host><pages><last>116</last><first>102</first></pages><author></author><title>Proceedings of CP'98, Principles and Practice of Constraint Programming</title><publicationDate>1998</publicationDate></host><title>Using Graph Decomposition for Solving Continuous CSPs</title><publicationDate>1998</publicationDate></json:item><json:item><author><json:item><name>L Blum</name></json:item><json:item><name>M Shub</name></json:item><json:item><name>S Smale</name></json:item></author><host><volume>21</volume><pages><first>1</first></pages><author></author><title>Bulletin of the AMS</title><publicationDate>1989-07</publicationDate></host><title>On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines</title><publicationDate>1989-07</publicationDate></json:item><json:item><host><author><json:item><name>H Boehm</name></json:item></author><title>Constructive Reals Calculator</title></host></json:item><json:item><author><json:item><name>R,P Brent</name></json:item></author><host><volume>4</volume><pages><last>70</last><first>57</first></pages><author></author><title>ACM Trans. Math. Software</title><publicationDate>1978</publicationDate></host><title>A Fortran multiple precision package</title><publicationDate>1978</publicationDate></json:item><json:item><author><json:item><name>V Brattka</name></json:item></author><host><volume>162</volume><pages><last>77</last><first>47</first></pages><author></author><title>Theoret. Comput. Sci</title><publicationDate>1996</publicationDate></host><title>Recursive characterisation of computable real-valued functions and relations</title><publicationDate>1996</publicationDate></json:item><json:item><author><json:item><name>V Brattka</name></json:item><json:item><name>P Hertling</name></json:item></author><host><volume>1649</volume><author></author><title>Informatik Berichte</title><publicationDate>1994</publicationDate></host><title>Continuity and Computability of Relations</title><publicationDate>1994</publicationDate></json:item><json:item><host><author><json:item><name>K Briggs</name></json:item><json:item><name> Xr</name></json:item></author></host></json:item><json:item><author><json:item><name>M Christie</name></json:item><json:item><name>E Languénou</name></json:item><json:item><name>L Granvilliers</name></json:item></author><host><pages><last>632</last><first>618</first></pages><author></author><title>Proceedings of CP'2002, Principles and Practice of Constraint Programming</title><publicationDate>2002</publicationDate></host><title>Modeling Camera Control with Constrained Hypertubes</title><publicationDate>2002</publicationDate></json:item><json:item><author><json:item><name>J,G Cleary</name></json:item></author><host><volume>2</volume><pages><last>149</last><first>125</first></pages><issue>2</issue><author></author><title>Future Computing Systems</title><publicationDate>1987</publicationDate></host><title>Logical Arithmetic</title><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>H Collavizza</name></json:item><json:item><name>F Delobel</name></json:item><json:item><name>M Rueher</name></json:item></author><host><volume>5</volume><pages><last>228</last><first>213</first></pages><issue>3</issue><author></author><title>Reliable Computing</title><publicationDate>1999</publicationDate></host><title>Comparing Partial Consistencies</title><publicationDate>1999</publicationDate></json:item><json:item><author><json:item><name>H Collavizza</name></json:item><json:item><name>F Delobel</name></json:item><json:item><name>M Rueher</name></json:item></author><host><pages><last>413</last><first>406</first></pages><author></author><title>Proceedings of IJCAI'99, International Joint Conference on Artificial Intelligence</title><publicationDate>1999</publicationDate></host><title>Extending Consistent Domains of Numeric CSP</title><publicationDate>1999</publicationDate></json:item><json:item><author><json:item><name>E Davis</name></json:item></author><host><volume>32</volume><pages><last>331</last><first>281</first></pages><author></author><title>Artificial Intelligence</title><publicationDate>1987</publicationDate></host><title>Constraint Propagation with Interval Labels</title><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>Y Deville</name></json:item><json:item><name>M Jansen</name></json:item><json:item><name>P Van Hentenryck</name></json:item></author><host><pages><last>176</last><first>162</first></pages><author></author><title>Proceedings of CP'1998, Principles and Practice of Constraint Programming</title><publicationDate>1998</publicationDate></host><title>Consistency Techniques in Ordinary Differential Equations</title><publicationDate>1998</publicationDate></json:item><json:item><host><author><json:item><name>A Edalat</name></json:item><json:item><name>R Heckmann</name></json:item></author><title>Computing with real numbers: (i) LFT approach to real computation, (ii) Domain-theoretic model of computational geometry</title><publicationDate>2002</publicationDate></host></json:item><json:item><host><author><json:item><name>L Errington</name></json:item><json:item><name>R Heckmann</name></json:item></author><title>Using the IC Reals library</title></host></json:item><json:item><author><json:item><name>S Ferson</name></json:item><json:item><name>L Ginzburg</name></json:item><json:item><name>V Kreinovich</name></json:item><json:item><name>L Longpré</name></json:item><json:item><name>M Aviles</name></json:item></author><host><volume>33</volume><pages><last>118</last><first>108</first></pages><author></author><title>ACM SIGACT News</title><publicationDate>2002</publicationDate></host><title>Computing Variance for Interval Data is NP-Hard</title><publicationDate>2002</publicationDate></json:item><json:item><author><json:item><name>X Fischer</name></json:item><json:item><name>J.-P Nadeau</name></json:item><json:item><name>P Sébastian</name></json:item><json:item><name>P Joyot</name></json:item></author><host><pages><last>42</last><first>35</first></pages><author></author><title>Proceedings of IDMME'2000, Integrated Design and Manufacturing in Mechanical Engineering Conference</title><publicationDate>2002</publicationDate></host><title>Qualitative Constraints in Integrated Design</title><publicationDate>2002</publicationDate></json:item><json:item><host><author><json:item><name>T Granlund</name></json:item></author></host></json:item><json:item><author><json:item><name>L Granvilliers</name></json:item></author><host><volume>7</volume><pages><last>483</last><first>467</first></pages><issue>6</issue><author></author><title>Reliable Computing</title><publicationDate>2001</publicationDate></host><title>On the Combination of Interval Constraint Solvers</title><publicationDate>2001</publicationDate></json:item><json:item><author><json:item><name>L Granvilliers</name></json:item><json:item><name>F Benhamou</name></json:item></author><host><volume>20</volume><pages><last>168</last><first>155</first></pages><issue>2</issue><author></author><title>Journal of Global Optimization</title><publicationDate>2001</publicationDate></host><title>Progress in the Solving of a Circuit Design Problem</title><publicationDate>2001</publicationDate></json:item><json:item><author><json:item><name>L Granvilliers</name></json:item><json:item><name>E Monfroy</name></json:item><json:item><name>F Benhamou</name></json:item></author><host><pages><last>166</last><first>150</first></pages><author></author><title>Proceedings of ISSAC'2001, International Symposium on Symbolic and Algebraic Computations</title><publicationDate>2001</publicationDate></host><title>Symbolic-Interval Cooperation in Constraint Programming</title><publicationDate>2001</publicationDate></json:item><json:item><author><json:item><name>E Hansen</name></json:item></author><host><volume>3</volume><pages><last>29</last><first>7</first></pages><author></author><title>Reliable Computing</title><publicationDate>1997</publicationDate></host><title>Sharpness in interval computations</title><publicationDate>1997</publicationDate></json:item><json:item><host><author><json:item><name>L Jaulin</name></json:item><json:item><name>M Kieffer</name></json:item><json:item><name>O Didrit</name></json:item><json:item><name>E Walter</name></json:item></author><title>Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics</title><publicationDate>2001</publicationDate></host></json:item><json:item><author><json:item><name>R,B Kearfott</name></json:item></author><host><author></author><title>Kluwer</title><publicationDate>1996</publicationDate></host><title>Rigorous Global Search: Continuous Problems</title><publicationDate>1996</publicationDate></json:item><json:item><host><author><json:item><name>R,B Kearfott</name></json:item><json:item><name>V Kreinovich</name></json:item></author><publicationDate>1996</publicationDate></host></json:item><json:item><author><json:item><name>K.-I Ko</name></json:item></author><host><author></author><title>Birkhäuser</title><publicationDate>1991</publicationDate></host><title>Complexity Theory of Real Functions</title><publicationDate>1991</publicationDate></json:item><json:item><author><json:item><name>V Kreinovich</name></json:item></author><host><author></author><title>Journal of Global Optimization</title></host><title>Probabilities, Intervals, What Next? Optimization Problems Related to Extension of Interval Computations to Situations with Partial Information about Probabilities</title></json:item><json:item><author><json:item><name>V Kreinovich</name></json:item><json:item><name>A Lakeyev</name></json:item><json:item><name>J Rohn</name></json:item><json:item><name>P Kahl</name></json:item></author><host><author></author><title>Computational Complexity and Feasibility of Data Processing and Interval Computations</title><publicationDate>1997</publicationDate></host><publicationDate>1997</publicationDate></json:item><json:item><host><author><json:item><name>U Kulisch</name></json:item></author><title>MemorandumMemorandum¨Memorandumüber Computer, Arithmetik und Numerik</title><publicationDate>1996</publicationDate></host></json:item><json:item><author><json:item><name>V,P Kuznetsov</name></json:item><json:item><name> Russian 38</name></json:item><json:item><name>Y Lebbah</name></json:item><json:item><name>M Rueher</name></json:item><json:item><name>C Michel</name></json:item></author><host><author></author><title>Proceedings of CP'2002, Principles and Practice of Constraint Programming</title><publicationDate>1991</publicationDate></host><title>Interval Statistical Models A Global Filtering Algorithm for Handling Systems of Quadratic Equations and Inequations</title><publicationDate>1991</publicationDate></json:item><json:item><host><author><json:item><name>M Lerch</name></json:item><json:item><name>G Tischler</name></json:item><json:item><name>J Wolff Von Gudenberg</name></json:item><json:item><name>W Hofschuster</name></json:item><json:item><name>W Krämer</name></json:item></author><title>The Interval Library filib++ 2.0 -Design, Features and Sample Programs</title><publicationDate>2001</publicationDate></host></json:item><json:item><author><json:item><name>O Lhomme</name></json:item></author><host><pages><last>238</last><first>232</first></pages><author></author><title>Proceedings of IJCAI'93, International Joint Conference of Artificial Intelligence</title><publicationDate>1993</publicationDate></host><title>Consistency Techniques for Numeric CSPs</title><publicationDate>1993</publicationDate></json:item><json:item><author><json:item><name>O Lhomme</name></json:item><json:item><name>A Gotlieb</name></json:item><json:item><name>M Rueher</name></json:item></author><host><volume>37</volume><pages><last>183</last><first>165</first></pages><issue>12</issue><author></author><title>Journal of Logic Programming</title><publicationDate>1998</publicationDate></host><title>Dynamic Optimization of Interval Narrowing Algorithms</title><publicationDate>1998</publicationDate></json:item><json:item><host><pages><first>43</first></pages><author><json:item><name>K Mehlhorn</name></json:item><json:item><name>S Näher</name></json:item><json:item><name>R,E Moore</name></json:item></author><title>Interval Analysis</title><publicationDate>1966</publicationDate></host></json:item><json:item><author><json:item><name>R,E Moore</name></json:item></author><host><author></author><title>Methods and Applications of Interval Analysis, SIAM</title><publicationDate>1979</publicationDate></host><publicationDate>1979</publicationDate></json:item><json:item><author><json:item><name>N Müller</name></json:item><json:item><name> Th</name></json:item></author><host><author></author><title>iRRAM -Exact Arithmetic in C++</title></host></json:item><json:item><host><author><json:item><name>N,S Nedialkov</name></json:item></author><title>Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation</title><publicationDate>1999</publicationDate></host></json:item><json:item><host><author><json:item><name>A Neumaier</name></json:item></author><title>Interval Methods for Systems of Equations</title><publicationDate>1990</publicationDate></host></json:item><json:item><author><json:item><name>P Nivlet</name></json:item><json:item><name>F Fournier</name></json:item><json:item><name>J Royer</name></json:item></author><host><pages><last>14</last><first>9</first></pages><author></author><title>Proceedings of the 71st Annual International Meeting of the Society of Exploratory Geophysics SEG</title><publicationDate>2001-09</publicationDate></host><title>A new methodology to account for uncertainties in 4-D seismic interpretation</title><publicationDate>2001-09</publicationDate></json:item><json:item><author><json:item><name>P Nivlet</name></json:item><json:item><name>F Fournier</name></json:item><json:item><name>J Royer</name></json:item></author><host><pages><first>71327</first></pages><author></author><title>Proceedings of the 2001 Society of Petroleum Engineers Annual Conference SPE</title><publicationDate>2001-09-30</publicationDate></host><title>Propagating interval uncertainties in supervised pattern recognition for reservoir characterization</title><publicationDate>2001-09-30</publicationDate></json:item><json:item><author><json:item><name>W Older</name></json:item><json:item><name>W Vellino</name></json:item><json:item><name>A </name></json:item></author><host><author></author><title>Constraint Logic Programming: Selected Research</title><publicationDate>1993</publicationDate></host><title>Constraint Arithmetic on Real Intervals</title><publicationDate>1993</publicationDate></json:item><json:item><host><author><json:item><name>O 'sullivan</name></json:item><json:item><name>B </name></json:item></author><title>Constraint-Aided Conceptual Design</title><publicationDate>1999</publicationDate></host></json:item><json:item><author><json:item><name>J.-F Puget</name></json:item><json:item><name>P Van Hentenryck</name></json:item></author><host><volume>13</volume><pages><last>93</last><first>75</first></pages><issue>1</issue><author></author><title>Journal of Global Optimization</title><publicationDate>1998</publicationDate></host><title>A Constraint Satisfaction Approach to a Circuit Design Problem</title><publicationDate>1998</publicationDate></json:item><json:item><host><author><json:item><name>S Rabinovich</name></json:item></author><title>Measurement Errors: Theory and Practice</title><publicationDate>1993</publicationDate></host></json:item><json:item><author><json:item><name>S Ratschan</name></json:item></author><host><pages><last>195</last><first>181</first></pages><author></author><title>Proceedings of AISC'2002, International Conference on Artificial Intelligence and Symbolic Computations</title><publicationDate>2002</publicationDate></host><title>Continuous First-Order Constraint Satisfaction</title><publicationDate>2002</publicationDate></json:item><json:item><host><author><json:item><name>N Revol</name></json:item><json:item><name>F Rouillier</name></json:item></author><title>Motivations for an arbitrary precision interval arithmetic and the MPFI library Research report R 2002-27</title><publicationDate>2002</publicationDate></host></json:item><json:item><author><json:item><name>D Richardson</name></json:item></author><host><pages><last>272</last><first>253</first></pages><author></author><title>Proceedings of CCA2000</title><publicationDate>2001</publicationDate></host><title>The Uniformity Conjecture</title><publicationDate>2001</publicationDate></json:item><json:item><author><json:item><name>N,C Rowe</name></json:item></author><host><volume>9</volume><pages><last>1113</last><first>1098</first></pages><author></author><title>SIAM Journal of Scientific Statistical Computing</title><publicationDate>1988</publicationDate></host><title>Absolute bounds on the mean and standard deviation of transformed data for constant-sign-derivative transformations</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>Sam Haroud</name></json:item><json:item><name>D Faltings</name></json:item><json:item><name>B </name></json:item></author><host><volume>1</volume><pages><last>118</last><first>85</first></pages><author></author><title>Constraints</title><publicationDate>1996</publicationDate></host><title>Consistency Techniques for Continuous Constraints</title><publicationDate>1996</publicationDate></json:item><json:item><author><json:item><name>P Van Hentenryck</name></json:item><json:item><name>Mc Allester</name></json:item><json:item><name>D Kapur</name></json:item><json:item><name>D </name></json:item></author><host><volume>34</volume><pages><last>827</last><first>797</first></pages><issue>2</issue><author></author><title>SIAM Journal on Numerical Analysis</title><publicationDate>1997</publicationDate></host><title>Solving Polynomial Systems using a Branch-and-Prune Approach</title><publicationDate>1997</publicationDate></json:item><json:item><host><author><json:item><name>P Van Hentenryck</name></json:item><json:item><name>L Michel</name></json:item><json:item><name>Y Deville</name></json:item></author><title>Numerica: a Modeling Language for Global Optimization</title><publicationDate>1997</publicationDate></host></json:item><json:item><host><author><json:item><name>S,A Vavasis</name></json:item></author><title>Nonlinear Optimization: Complexity Issues</title><publicationDate>1991</publicationDate></host></json:item><json:item><host><author><json:item><name>P Walley</name></json:item></author><title>Statistical Reasoning with Imprecise Probabilities, Chapman and Hall</title><publicationDate>1991</publicationDate></host></json:item><json:item><host><author><json:item><name>K Weihrauch</name></json:item></author><title>Computable Analysis. An Introduction</title><publicationDate>2000</publicationDate></host></json:item><json:item><author><json:item><name>K Yamamura</name></json:item><json:item><name>H Kawata</name></json:item><json:item><name>A Tokue</name></json:item></author><host><volume>38</volume><pages><last>201</last><first>188</first></pages><author></author><title>BIT</title><publicationDate>1998</publicationDate></host><title>Interval Analysis using Linear Programming</title><publicationDate>1998</publicationDate></json:item><json:item><host><author><json:item><name>G Xiang</name></json:item></author></host></json:item><json:item><author><json:item><name>P Zimmermann</name></json:item></author><host><pages><last>89</last><first>2000</first></pages><author></author><title>4th Conference on Real Numbers and Computers</title></host><title>MPFR: A Library for Multiprecision Floating-Point Arithmetic with Exact Rounding</title></json:item></refBibs><genre><json:string>conference</json:string></genre><serie><editor><json:item><name>Gerhard Goos</name><affiliations><json:string>Karlsruhe University, Germany</json:string></affiliations></json:item><json:item><name>Juris Hartmanis</name><affiliations><json:string>Cornell University, NY, USA</json:string></affiliations></json:item><json:item><name>Jan van Leeuwen</name><affiliations><json:string>Utrecht University, The Netherlands</json:string></affiliations></json:item></editor><issn><json:string>0302-9743</json:string></issn><language><json:string>unknown</json:string></language><eissn><json:string>1611-3349</json:string></eissn><title>Lecture Notes in Computer Science</title><copyrightDate>2004</copyrightDate></serie><host><editor><json:item><name>René Alt</name><affiliations><json:string>CNRS, UMR 7606, LIP6, University Pierre et Marie Curie, 4 place Jussieu, 75252, Paris cedex 05, France</json:string><json:string>E-mail: Rene.Alt@lip6.fr</json:string></affiliations></json:item><json:item><name>Andreas Frommer</name><affiliations><json:string>Fachbereich C, Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gauss-Straße 20, 42097, Wuppertal, Germany</json:string><json:string>E-mail: frommer@math.uni-wuppertal.de</json:string></affiliations></json:item><json:item><name>R. Baker Kearfott</name><affiliations><json:string>University of Louisiana at Lafayette,</json:string><json:string>E-mail: rbk@louisiana.edu</json:string></affiliations></json:item><json:item><name>Wolfram Luther</name><affiliations><json:string>Universität Duisburg-Essen, 47048, Duisburg, Germany</json:string><json:string>E-mail: luther@informatik.uni-duisburg.de</json:string></affiliations></json:item></editor><subject><json:item><value>Computer Science</value></json:item><json:item><value>Computer Science</value></json:item><json:item><value>Numeric Computing</value></json:item><json:item><value>Software Engineering</value></json:item><json:item><value>Programming Languages, Compilers, Interpreters</value></json:item><json:item><value>Algorithm Analysis and Problem Complexity</value></json:item><json:item><value>Mathematical Software</value></json:item><json:item><value>Numerical Analysis</value></json:item></subject><isbn><json:string>978-3-540-21260-7</json:string></isbn><language><json:string>unknown</json:string></language><eissn><json:string>1611-3349</json:string></eissn><title>Numerical Software with Result Verification</title><bookId><json:string>978-3-540-24738-8</json:string></bookId><volume>2991</volume><pages><last>305</last><first>274</first></pages><issn><json:string>0302-9743</json:string></issn><genre><json:string>book-series</json:string></genre><eisbn><json:string>978-3-540-24738-8</json:string></eisbn><copyrightDate>2004</copyrightDate><doi><json:string>10.1007/b96498</json:string></doi></host><publicationDate>2004</publicationDate><copyrightDate>2004</copyrightDate><doi><json:string>10.1007/978-3-540-24738-8_17</json:string></doi><id>54E3EE5AE7FA9EAB35FD40CC7300C9AF1867217F</id><score>0.3101355</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/54E3EE5AE7FA9EAB35FD40CC7300C9AF1867217F/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/54E3EE5AE7FA9EAB35FD40CC7300C9AF1867217F/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/54E3EE5AE7FA9EAB35FD40CC7300C9AF1867217F/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Novel Approaches to Numerical Software with Result Verification</title><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><availability><p>Springer-Verlag Berlin Heidelberg, 2004</p></availability><date>2004</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Novel Approaches to Numerical Software with Result Verification</title><author xml:id="author-1"><persName><forename type="first">Laurent</forename><surname>Granvilliers</surname></persName><email>granvilliers@irin.univ-nantes.fr</email><affiliation>IRIN, Université de Nantes, France</affiliation></author><author xml:id="author-2"><persName><forename type="first">Vladik</forename><surname>Kreinovich</surname></persName><email>vladik@cs.utep.edu</email><affiliation>Department of Computer Science, University of Texas at El Paso, 79968, El Paso, TX, USA</affiliation></author><author xml:id="author-3"><persName><forename type="first">Norbert</forename><surname>Müller</surname></persName><email>mueller@uni-trier.de</email><affiliation>Abteilung Informatik, Universität Trier, 54286, Trier, Germany</affiliation></author></analytic><monogr><title level="m">Numerical Software with Result Verification</title><title level="m" type="sub">International Dagstuhl Seminar, Dagstuhl Castle, Germany, January 19-24, 2003. Revised Papers</title><idno type="pISBN">978-3-540-21260-7</idno><idno type="eISBN">978-3-540-24738-8</idno><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="DOI">10.1007/b96498</idno><idno type="book-ID">978-3-540-24738-8</idno><idno type="book-title-ID">82036</idno><idno type="book-sequence-number">2991</idno><idno type="book-volume-number">2991</idno><idno type="book-chapter-count">18</idno><editor><persName><forename type="first">René</forename><surname>Alt</surname></persName><email>Rene.Alt@lip6.fr</email><affiliation>CNRS, UMR 7606, LIP6, University Pierre et Marie Curie, 4 place Jussieu, 75252, Paris cedex 05, France</affiliation></editor><editor><persName><forename type="first">Andreas</forename><surname>Frommer</surname></persName><email>frommer@math.uni-wuppertal.de</email><affiliation>Fachbereich C, Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gauss-Straße 20, 42097, Wuppertal, Germany</affiliation></editor><editor><persName><forename type="first">R.</forename><forename type="first">Baker</forename><surname>Kearfott</surname></persName><email>rbk@louisiana.edu</email><affiliation>University of Louisiana at Lafayette,</affiliation></editor><editor><persName><forename type="first">Wolfram</forename><surname>Luther</surname></persName><email>luther@informatik.uni-duisburg.de</email><affiliation>Universität Duisburg-Essen, 47048, Duisburg, Germany</affiliation></editor><imprint><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><date type="published" when="2004"></date><biblScope unit="volume">2991</biblScope><biblScope unit="page" from="274">274</biblScope><biblScope unit="page" to="305">305</biblScope></imprint></monogr><series><title level="s">Lecture Notes in Computer Science</title><editor><persName><forename type="first">Gerhard</forename><surname>Goos</surname></persName><affiliation>Karlsruhe University, Germany</affiliation></editor><editor><persName><forename type="first">Juris</forename><surname>Hartmanis</surname></persName><affiliation>Cornell University, NY, USA</affiliation></editor><editor><persName><forename type="first">Jan</forename><surname>van Leeuwen</surname></persName><affiliation>Utrecht University, The Netherlands</affiliation></editor><biblScope><date>2004</date></biblScope><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="series-Id">558</idno></series><idno type="istex">54E3EE5AE7FA9EAB35FD40CC7300C9AF1867217F</idno><idno type="DOI">10.1007/978-3-540-24738-8_17</idno><idno type="ChapterID">17</idno><idno type="ChapterID">Chap17</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2004</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: Traditional design of numerical software with result verification is based on the assumption that we know the algorithm f(x 1,...,x n ) that transforms inputs x 1,...,x n into the output y=f(x 1,...,x n ), and we know the intervals of possible values of the inputs. Many real-life problems go beyond this paradigm. In some cases, we do not have an algorithm f, we only know some relation (constraints) between x i and y. In other cases, in addition to knowing the intervals x i , we may know some relations between x i ; we may have some information about the probabilities of different values of x i , and we may know the exact values of some of the inputs (e.g., we may know that x 1 = π/2). In this paper, we describe the approaches for solving these real-life problems. In Section 2, we describe interval consistency techniques related to handling constraints; in Section 3, we describe techniques that take probabilistic information into consideration, and in Section 4, we overview techniques for processing exact real numbers.</p></abstract><textClass><keywords scheme="Book-Subject-Collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass><keywords scheme="Book-Subject-Group"><list><label>I</label><label>I1701X</label><label>I14029</label><label>I14037</label><label>I16021</label><label>M14042</label><label>M14050</label><item><term>Computer Science</term></item><item><term>Numeric Computing</term></item><item><term>Software Engineering</term></item><item><term>Programming Languages, Compilers, Interpreters</term></item><item><term>Algorithm Analysis and Problem Complexity</term></item><item><term>Mathematical Software</term></item><item><term>Numerical Analysis</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2004">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-11-22">References added</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-20">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/54E3EE5AE7FA9EAB35FD40CC7300C9AF1867217F/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Springer, Publisher found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType><istex:document><Publisher><PublisherInfo><PublisherName>Springer Berlin Heidelberg</PublisherName><PublisherLocation>Berlin, Heidelberg</PublisherLocation></PublisherInfo><Series><SeriesInfo SeriesType="Series" TocLevels="0"><SeriesID>558</SeriesID><SeriesPrintISSN>0302-9743</SeriesPrintISSN><SeriesElectronicISSN>1611-3349</SeriesElectronicISSN><SeriesTitle Language="En">Lecture Notes in Computer Science</SeriesTitle></SeriesInfo><SeriesHeader><EditorGroup><Editor AffiliationIDS="Aff1"><EditorName DisplayOrder="Western"><GivenName>Gerhard</GivenName><FamilyName>Goos</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff2"><EditorName DisplayOrder="Western"><GivenName>Juris</GivenName><FamilyName>Hartmanis</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff3"><EditorName DisplayOrder="Western"><GivenName>Jan</GivenName><Particle>van</Particle><FamilyName>Leeuwen</FamilyName></EditorName></Editor><Affiliation ID="Aff1"><OrgName>Karlsruhe University</OrgName><OrgAddress><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>Cornell University</OrgName><OrgAddress><State>NY</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgName>Utrecht University</OrgName><OrgAddress><Country>The Netherlands</Country></OrgAddress></Affiliation></EditorGroup></SeriesHeader><Book Language="En"><BookInfo BookProductType="Proceedings" ContainsESM="No" Language="En" MediaType="eBook" NumberingDepth="2" NumberingStyle="ContentOnly" OutputMedium="All" TocLevels="0"><BookID>978-3-540-24738-8</BookID><BookTitle>Numerical Software with Result Verification</BookTitle><BookSubTitle>International Dagstuhl Seminar, Dagstuhl Castle, Germany, January 19-24, 2003. Revised Papers</BookSubTitle><BookVolumeNumber>2991</BookVolumeNumber><BookSequenceNumber>2991</BookSequenceNumber><BookDOI>10.1007/b96498</BookDOI><BookTitleID>82036</BookTitleID><BookPrintISBN>978-3-540-21260-7</BookPrintISBN><BookElectronicISBN>978-3-540-24738-8</BookElectronicISBN><BookChapterCount>18</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2004</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I1701X" Priority="1" Type="Secondary">Numeric Computing</BookSubject><BookSubject Code="I14029" Priority="2" Type="Secondary">Software Engineering</BookSubject><BookSubject Code="I14037" Priority="3" Type="Secondary">Programming Languages, Compilers, Interpreters</BookSubject><BookSubject Code="I16021" Priority="4" Type="Secondary">Algorithm Analysis and Problem Complexity</BookSubject><BookSubject Code="M14042" Priority="5" Type="Secondary">Mathematical Software</BookSubject><BookSubject Code="M14050" Priority="6" Type="Secondary">Numerical Analysis</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff4"><EditorName DisplayOrder="Western"><GivenName>René</GivenName><FamilyName>Alt</FamilyName></EditorName><Contact><Email>Rene.Alt@lip6.fr</Email></Contact></Editor><Editor AffiliationIDS="Aff5"><EditorName DisplayOrder="Western"><GivenName>Andreas</GivenName><FamilyName>Frommer</FamilyName></EditorName><Contact><Email>frommer@math.uni-wuppertal.de</Email></Contact></Editor><Editor AffiliationIDS="Aff6"><EditorName DisplayOrder="Western"><GivenName>R.</GivenName><GivenName>Baker</GivenName><FamilyName>Kearfott</FamilyName></EditorName><Contact><Email>rbk@louisiana.edu</Email></Contact></Editor><Editor AffiliationIDS="Aff7"><EditorName DisplayOrder="Western"><GivenName>Wolfram</GivenName><FamilyName>Luther</FamilyName></EditorName><Contact><Email>luther@informatik.uni-duisburg.de</Email></Contact></Editor><Affiliation ID="Aff4"><OrgDivision>CNRS, UMR 7606, LIP6</OrgDivision><OrgName>University Pierre et Marie Curie</OrgName><OrgAddress><Street>4 place Jussieu</Street><Postcode>75252</Postcode><City>Paris cedex 05</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff5"><OrgDivision>Fachbereich C, Mathematik und Naturwissenschaften</OrgDivision><OrgName>Bergische Universität Wuppertal</OrgName><OrgAddress><Street>Gauss-Straße 20</Street><Postcode>42097</Postcode><City>Wuppertal</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff6"><OrgName>University of Louisiana at Lafayette</OrgName><OrgAddress><Country> </Country></OrgAddress></Affiliation><Affiliation ID="Aff7"><OrgName>Universität Duisburg-Essen</OrgName><OrgAddress><Postcode>47048</Postcode><City>Duisburg</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part5"><PartInfo TocLevels="0"><PartID>5</PartID><PartSequenceNumber>5</PartSequenceNumber><PartTitle>Novel Approaches to Verification</PartTitle><PartChapterCount>3</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Numerical Software with Result Verification</BookTitle></PartContext></PartInfo><Chapter ID="Chap17" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>17</ChapterID><ChapterDOI>10.1007/978-3-540-24738-8_17</ChapterDOI><ChapterSequenceNumber>17</ChapterSequenceNumber><ChapterTitle Language="En">Novel Approaches to Numerical Software with Result Verification</ChapterTitle><ChapterFirstPage>274</ChapterFirstPage><ChapterLastPage>305</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2004</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><PartID>5</PartID><BookID>978-3-540-24738-8</BookID><BookTitle>Numerical Software with Result Verification</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff8"><AuthorName DisplayOrder="Western"><GivenName>Laurent</GivenName><FamilyName>Granvilliers</FamilyName></AuthorName><Contact><Email>granvilliers@irin.univ-nantes.fr</Email></Contact></Author><Author AffiliationIDS="Aff9"><AuthorName DisplayOrder="Western"><GivenName>Vladik</GivenName><FamilyName>Kreinovich</FamilyName></AuthorName><Contact><Email>vladik@cs.utep.edu</Email></Contact></Author><Author AffiliationIDS="Aff10"><AuthorName DisplayOrder="Western"><GivenName>Norbert</GivenName><FamilyName>Müller</FamilyName></AuthorName><Contact><Email>mueller@uni-trier.de</Email></Contact></Author><Affiliation ID="Aff8"><OrgDivision>IRIN</OrgDivision><OrgName>Université de Nantes</OrgName><OrgAddress><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff9"><OrgDivision>Department of Computer Science</OrgDivision><OrgName>University of Texas at El Paso</OrgName><OrgAddress><City>El Paso</City><State>TX</State><Postcode>79968</Postcode><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff10"><OrgDivision>Abteilung Informatik</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><Postcode>54286</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Traditional design of numerical software with result verification is based on the assumption that we know the algorithm <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">x</Emphasis><Subscript>1</Subscript>,...,<Emphasis Type="Italic">x</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>) that transforms inputs <Emphasis Type="Italic">x</Emphasis><Subscript>1</Subscript>,...,<Emphasis Type="Italic">x</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> into the output <Emphasis Type="Italic">y</Emphasis>=<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">x</Emphasis><Subscript>1</Subscript>,...,<Emphasis Type="Italic">x</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>), and we know the intervals of possible values of the inputs. Many real-life problems go beyond this paradigm. In some cases, we do not have an algorithm <Emphasis Type="Italic">f</Emphasis>, we only know some relation (constraints) between <Emphasis Type="Italic">x</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript> and <Emphasis Type="Italic">y</Emphasis>. In other cases, in addition to knowing the intervals <Emphasis Type="Italic">x</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript>, we may know some relations between <Emphasis Type="Italic">x</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript>; we may have some information about the probabilities of different values of <Emphasis Type="Italic">x</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript>, and we may know the exact values of some of the inputs (e.g., we may know that <Emphasis Type="Italic">x</Emphasis><Subscript>1</Subscript> = <Emphasis Type="Italic">π</Emphasis>/2). In this paper, we describe the approaches for solving these real-life problems. In Section 2, we describe interval consistency techniques related to handling constraints; in Section 3, we describe techniques that take probabilistic information into consideration, and in Section 4, we overview techniques for processing exact real numbers.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Novel Approaches to Numerical Software with Result Verification</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Novel Approaches to Numerical Software with Result Verification</title></titleInfo><name type="personal"><namePart type="given">Laurent</namePart><namePart type="family">Granvilliers</namePart><affiliation>IRIN, Université de Nantes, France</affiliation><affiliation>E-mail: granvilliers@irin.univ-nantes.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Vladik</namePart><namePart type="family">Kreinovich</namePart><affiliation>Department of Computer Science, University of Texas at El Paso, 79968, El Paso, TX, USA</affiliation><affiliation>E-mail: vladik@cs.utep.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Norbert</namePart><namePart type="family">Müller</namePart><affiliation>Abteilung Informatik, Universität Trier, 54286, Trier, Germany</affiliation><affiliation>E-mail: mueller@uni-trier.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="conference" displayLabel="OriginalPaper"></genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2004</dateIssued><copyrightDate encoding="w3cdtf">2004</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Abstract: Traditional design of numerical software with result verification is based on the assumption that we know the algorithm f(x 1,...,x n ) that transforms inputs x 1,...,x n into the output y=f(x 1,...,x n ), and we know the intervals of possible values of the inputs. Many real-life problems go beyond this paradigm. In some cases, we do not have an algorithm f, we only know some relation (constraints) between x i and y. In other cases, in addition to knowing the intervals x i , we may know some relations between x i ; we may have some information about the probabilities of different values of x i , and we may know the exact values of some of the inputs (e.g., we may know that x 1 = π/2). In this paper, we describe the approaches for solving these real-life problems. In Section 2, we describe interval consistency techniques related to handling constraints; in Section 3, we describe techniques that take probabilistic information into consideration, and in Section 4, we overview techniques for processing exact real numbers.</abstract><relatedItem type="host"><titleInfo><title>Numerical Software with Result Verification</title><subTitle>International Dagstuhl Seminar, Dagstuhl Castle, Germany, January 19-24, 2003. Revised Papers</subTitle></titleInfo><name type="personal"><namePart type="given">René</namePart><namePart type="family">Alt</namePart><affiliation>CNRS, UMR 7606, LIP6, University Pierre et Marie Curie, 4 place Jussieu, 75252, Paris cedex 05, France</affiliation><affiliation>E-mail: Rene.Alt@lip6.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Andreas</namePart><namePart type="family">Frommer</namePart><affiliation>Fachbereich C, Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gauss-Straße 20, 42097, Wuppertal, Germany</affiliation><affiliation>E-mail: frommer@math.uni-wuppertal.de</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">R.</namePart><namePart type="given">Baker</namePart><namePart type="family">Kearfott</namePart><affiliation>University of Louisiana at Lafayette</affiliation><affiliation>E-mail: rbk@louisiana.edu</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Wolfram</namePart><namePart type="family">Luther</namePart><affiliation>Universität Duisburg-Essen, 47048, Duisburg, Germany</affiliation><affiliation>E-mail: luther@informatik.uni-duisburg.de</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2004</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I1701X">Numeric Computing</topic><topic authority="SpringerSubjectCodes" authorityURI="I14029">Software Engineering</topic><topic authority="SpringerSubjectCodes" authorityURI="I14037">Programming Languages, Compilers, Interpreters</topic><topic authority="SpringerSubjectCodes" authorityURI="I16021">Algorithm Analysis and Problem Complexity</topic><topic authority="SpringerSubjectCodes" authorityURI="M14042">Mathematical Software</topic><topic authority="SpringerSubjectCodes" authorityURI="M14050">Numerical Analysis</topic></subject><identifier type="DOI">10.1007/b96498</identifier><identifier type="ISBN">978-3-540-21260-7</identifier><identifier type="eISBN">978-3-540-24738-8</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">82036</identifier><identifier type="BookID">978-3-540-24738-8</identifier><identifier type="BookChapterCount">18</identifier><identifier type="BookVolumeNumber">2991</identifier><identifier type="BookSequenceNumber">2991</identifier><identifier type="PartChapterCount">3</identifier><part><date>2004</date><detail type="part"><title>Novel Approaches to Verification</title></detail><detail type="volume"><number>2991</number><caption>vol.</caption></detail><extent unit="pages"><start>274</start><end>305</end></extent></part><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2004</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Goos</namePart><affiliation>Karlsruhe University, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Juris</namePart><namePart type="family">Hartmanis</namePart><affiliation>Cornell University, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jan</namePart><namePart type="family">van Leeuwen</namePart><affiliation>Utrecht University, The Netherlands</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><copyrightDate encoding="w3cdtf">2004</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2004</recordOrigin></recordInfo></relatedItem><identifier type="istex">54E3EE5AE7FA9EAB35FD40CC7300C9AF1867217F</identifier><identifier type="DOI">10.1007/978-3-540-24738-8_17</identifier><identifier type="ChapterID">17</identifier><identifier type="ChapterID">Chap17</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 2004</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 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