Novel Approaches to Numerical Software with Result Verification
Identifieur interne : 001898 ( Main/Exploration ); précédent : 001897; suivant : 001899Novel Approaches to Numerical Software with Result Verification
Auteurs : Laurent Granvilliers [France] ; Vladik Kreinovich [États-Unis] ; Norbert Müller [Allemagne]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2004.
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- Pascal (Inist)
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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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logiciel</term><term>Entrée sortie</term><term>Nombre réel</term><term>Paradigme</term><term>Satisfaction contrainte</term><term>Traitement contrainte</term><term>Vérification programme</term></keywords></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. 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