Basic concepts in numerical error analysis (suggested by linear algebra problems)
Andrzej Kiełbasiński (1978)
Banach Center Publications
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Andrzej Kiełbasiński (1978)
Banach Center Publications
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Stetter, Hans J.
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Codenotti, Bruno (1985-1986)
Portugaliae mathematica
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Florent de Dinechin, Christoph Lauter, Jean-Michel Muller (2007)
RAIRO - Theoretical Informatics and Applications
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This article is a case study in the implementation of a portable, proven and efficient correctly rounded elementary function in double-precision. We describe the methodology used to achieve these goals in the library. There are two novel aspects to this approach. The first is the proof framework, and in general the techniques used to balance performance and provability. The second is the introduction of processor-specific optimization to get performance equivalent to the best...
Guillaume Melquiond, Sylvain Pion (2007)
RAIRO - Theoretical Informatics and Applications
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Floating-point arithmetic provides a fast but inexact way of computing geometric predicates. In order for these predicates to be exact, it is important to rule out all the numerical situations where floating-point computations could lead to wrong results. Taking into account all the potential problems is a tedious work to do by hand. We study in this paper a floating-point implementation of a filter for the orientation-2 predicate, and how a formal and partially automatized verification...