An algorithm for chebyshev approximation by rationals with constrained denominators
Identifieur interne : 001108 ( Istex/Corpus ); précédent : 001107; suivant : 001109An algorithm for chebyshev approximation by rationals with constrained denominators
Auteurs : M. GugatSource :
- Constructive Approximation [ 0176-4276 ] ; 1996-06-01.
Abstract
Abstract: The problem of rational approximation is facilitated by introducing both lower and upper bounds on the denominators. For a general fractional inf-sup problem with constrained denominators, a differential correction algorithm and convergence results are given. Numerical examples are presented. The proposed algorithm has certain advantages compared with the original differential correction method: not only upper but also lower bounds for the optimal value are computed, linear convergence is always guaranteed, and due to a different start convergence is more rapid.
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DOI: 10.1007/BF02433040
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Gugat</name><affiliation><mods:affiliation>Department of Mathematics, University of Trier, 54286, Trier, Germany</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:FC3A95E05FAE56E94E64ED7102A92326A05EECC7</idno><date when="1996" year="1996">1996</date><idno type="doi">10.1007/BF02433040</idno><idno type="url">https://api.istex.fr/document/FC3A95E05FAE56E94E64ED7102A92326A05EECC7/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001108</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001108</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">An algorithm for chebyshev approximation by rationals with constrained denominators</title><author><name sortKey="Gugat, M" sort="Gugat, M" uniqKey="Gugat M" first="M." last="Gugat">M. Gugat</name><affiliation><mods:affiliation>Department of Mathematics, University of Trier, 54286, Trier, Germany</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Constructive Approximation</title><title level="j" type="abbrev">Constr. Approx</title><idno type="ISSN">0176-4276</idno><idno type="eISSN">1432-0940</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>New York</pubPlace><date type="published" when="1996-06-01">1996-06-01</date><biblScope unit="volume">12</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="197">197</biblScope><biblScope unit="page" to="221">221</biblScope></imprint><idno type="ISSN">0176-4276</idno></series><idno type="istex">FC3A95E05FAE56E94E64ED7102A92326A05EECC7</idno><idno type="DOI">10.1007/BF02433040</idno><idno type="ArticleID">BF02433040</idno><idno type="ArticleID">Art3</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0176-4276</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The problem of rational approximation is facilitated by introducing both lower and upper bounds on the denominators. For a general fractional inf-sup problem with constrained denominators, a differential correction algorithm and convergence results are given. Numerical examples are presented. The proposed algorithm has certain advantages compared with the original differential correction method: not only upper but also lower bounds for the optimal value are computed, linear convergence is always guaranteed, and due to a different start convergence is more rapid.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>M. 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The proposed algorithm has certain advantages compared with the original differential correction method: not only upper but also lower bounds for the optimal value are computed, linear convergence is always guaranteed, and due to a different start convergence is more rapid.</abstract><qualityIndicators><score>5.972</score><pdfVersion>1.3</pdfVersion><pdfPageSize>432 x 684 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>578</abstractCharCount><pdfWordCount>10508</pdfWordCount><pdfCharCount>44843</pdfCharCount><pdfPageCount>25</pdfPageCount><abstractWordCount>81</abstractWordCount></qualityIndicators><title>An algorithm for chebyshev approximation by rationals with constrained denominators</title><refBibs><json:item><author><json:item><name>@bullet </name></json:item><json:item><name>Barr@bulletdale@bullet,M J D@bullet P@bulletwell@bullet</name></json:item><json:item><name>E,D K R@bulletberts</name></json:item></author><host><volume>9</volume><pages><last>504</last><first>493</first></pages><author></author><title>SIAM J. Numer. Anal</title></host><title>The di@BULLETerential c@BULLETrrecti@BULLETn alg@BULLETrithm f@BULLETr rational l~ approximation</title></json:item><json:item><author><json:item><name>E,W Cheney</name></json:item></author><host><author></author><title>Introduction to Approximation Theory</title><publicationDate>1966</publicationDate></host><publicationDate>1966</publicationDate></json:item><json:item><author><json:item><name>E,W Cheney</name></json:item><json:item><name>H,L Loeb</name></json:item></author><host><volume>3</volume><pages><last>75</last><first>72</first></pages><author></author><title>Numer. Math</title><publicationDate>1961</publicationDate></host><title>Two new algorithms for rational approximation</title><publicationDate>1961</publicationDate></json:item><json:item><author><json:item><name>E,W J D Cheney@bulletm</name></json:item></author><host><volume>3</volume><pages><last>256</last><first>249</first></pages><author></author><title>Constr. Approx</title></host><title>P@BULLETwELL(@BULLET987):Thedi@BULLETerentialc@BULLETrrecti@BULLETnalg@BULLETrithmf@BULLETrgeneralizedrati@BULLETna@BULLET functions</title></json:item><json:item><host><author><json:item><name>L Chong</name></json:item><json:item><name>G,A Watson</name></json:item></author><title>Strong uniqueness in restricted rational approximation</title><publicationDate>1995</publicationDate></host></json:item><json:item><author><json:item><name>J,P Crouzeix</name></json:item><json:item><name>J,A Ferland</name></json:item></author><host><volume>52</volume><pages><last>207</last><first>191</first></pages><author></author><title>Math. Programming</title><publicationDate>1991</publicationDate></host><title>Algorithms for generalized fractional programming</title><publicationDate>1991</publicationDate></json:item><json:item><author><json:item><name>S,N Dua</name></json:item><json:item><name>H,L Loeb</name></json:item></author><host><volume>10</volume><pages><last>126</last><first>123</first></pages><author></author><title>SIAM J. Numer. Anal</title><publicationDate>1973</publicationDate></host><title>Further remarks on the differential correction algorithm</title><publicationDate>1973</publicationDate></json:item><json:item><author><json:item><name>C Dunham</name></json:item></author><host><volume>37</volume><pages><last>11</last><first>5</first></pages><author></author><title>J. Approx . Theory</title><publicationDate>1983</publicationDate></host><title>Chebyshev approximation by rationals with constrained denominators</title><publicationDate>1983</publicationDate></json:item><json:item><author><json:item><name>M Gugat</name></json:item></author><host><author></author><title>Numer. Algorithms</title></host><title>The Newton differential correction algorithm for uniform rational approximation</title></json:item><json:item><author><json:item><name>R Hettich</name></json:item><json:item><name>P Zencke</name></json:item></author><host><volume>27</volume><pages><last>1033</last><first>1024</first></pages><author></author><title>SIAM J. Numer. Anal</title><publicationDate>1990</publicationDate></host><title>An algorithm for general restricted rational Chebyshev approximation</title><publicationDate>1990</publicationDate></json:item><json:item><author><json:item><name>E,H Kaufmann</name></json:item><json:item><name>G,D Taylor</name></json:item></author><host><volume>32</volume><pages><last>26</last><first>9</first></pages><author></author><title>J. Approx. Theory</title><publicationDate>1981</publicationDate></host><title>Uniform approximation by rational functions having restricted denominators</title><publicationDate>1981</publicationDate></json:item><json:item><author><json:item><name>C,M Lee</name></json:item><json:item><name>F,D K Roberts</name></json:item></author><host><volume>27</volume><pages><last>121</last><first>111</first></pages><author></author><title>Math. Comp</title><publicationDate>1973</publicationDate></host><title>A comparison of algorithms for rational l~ approximation</title><publicationDate>1973</publicationDate></json:item><json:item><author><json:item><name>P Zencke</name></json:item><json:item><name>R Hettich</name></json:item></author><host><volume>38</volume><pages><last>340</last><first>323</first></pages><author></author><title>Math. 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For a general fractional inf-sup problem with constrained denominators, a differential correction algorithm and convergence results are given. Numerical examples are presented. The proposed algorithm has certain advantages compared with the original differential correction method: not only upper but also lower bounds for the optimal value are computed, linear convergence is always guaranteed, and due to a different start convergence is more rapid.</p></abstract><textClass><keywords scheme="Journal Subject"><list><head>Mathematics</head><item><term>Analysis</term></item><item><term>Numerical Analysis</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1994-01-29">Created</change><change when="1996-06-01">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/FC3A95E05FAE56E94E64ED7102A92326A05EECC7/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-Verlag</PublisherName><PublisherLocation>New York</PublisherLocation></PublisherInfo><Journal><JournalInfo JournalProductType="ArchiveJournal" NumberingStyle="Unnumbered"><JournalID>365</JournalID><JournalPrintISSN>0176-4276</JournalPrintISSN><JournalElectronicISSN>1432-0940</JournalElectronicISSN><JournalTitle>Constructive Approximation</JournalTitle><JournalAbbreviatedTitle>Constr. 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For a general fractional inf-sup problem with constrained denominators, a differential correction algorithm and convergence results are given. Numerical examples are presented. The proposed algorithm has certain advantages compared with the original differential correction method: not only upper but also lower bounds for the optimal value are computed, linear convergence is always guaranteed, and due to a different start convergence is more rapid.</Para></Abstract><KeywordGroup Language="En"><Heading>AMS classification</Heading><Keyword>41A20</Keyword><Keyword>65D15</Keyword><Keyword>90C32</Keyword><Keyword>90C34</Keyword></KeywordGroup><KeywordGroup Language="En"><Heading>Key words and phrases</Heading><Keyword>Chebyshev approximation</Keyword><Keyword>Rational approximation</Keyword><Keyword>Constrained denominators</Keyword><Keyword>Differential correction algorithm</Keyword><Keyword>Fractional programming</Keyword></KeywordGroup><ArticleNote Type="CommunicatedBy"><SimplePara>Communicated by M. J. D. Powell</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>An algorithm for chebyshev approximation by rationals with constrained denominators</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>An algorithm for chebyshev approximation by rationals with constrained denominators</title></titleInfo><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Gugat</namePart><affiliation>Department of Mathematics, University of Trier, 54286, Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper"></genre><originInfo><publisher>Springer-Verlag</publisher><place><placeTerm type="text">New York</placeTerm></place><dateCreated encoding="w3cdtf">1994-01-29</dateCreated><dateIssued encoding="w3cdtf">1996-06-01</dateIssued><copyrightDate encoding="w3cdtf">1996</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: The problem of rational approximation is facilitated by introducing both lower and upper bounds on the denominators. For a general fractional inf-sup problem with constrained denominators, a differential correction algorithm and convergence results are given. Numerical examples are presented. The proposed algorithm has certain advantages compared with the original differential correction method: not only upper but also lower bounds for the optimal value are computed, linear convergence is always guaranteed, and due to a different start convergence is more rapid.</abstract><relatedItem type="host"><titleInfo><title>Constructive Approximation</title></titleInfo><titleInfo type="abbreviated"><title>Constr. 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