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Journal Articles Journal of Automated Reasoning Year : 2015

Formal Proofs of Rounding Error Bounds

Abstract

Floating-point arithmetic is a very efficient solution to perform computa-tions in the real field. However, it induces rounding errors making results computed in floating-point differ from what would be computed with reals. Although numerical analysis gives tools to bound such differences, the proofs involved can be painful, hence error prone. We thus investigate the ability of a proof assistant like Coq to mechanically check such proofs. We demonstrate two different results involving ma-trices, which are pervasive among numerical algorithms, and show that a large part of the development effort can be shared between them.
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Dates and versions

hal-01091189 , version 1 (04-12-2014)
hal-01091189 , version 2 (26-08-2015)

Identifiers

Cite

Pierre Roux. Formal Proofs of Rounding Error Bounds: With application to an automatic positive definiteness check. Journal of Automated Reasoning, 2015, pp.23. ⟨10.1007/s10817-015-9339-z⟩. ⟨hal-01091189v2⟩
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