Error-Free Transformations in Real and Complex Floating Point Arithmetic

Abstract : Error-free transformation is a concept that makes it possible to compute accurate results within a floating point arithmetic. Up to now, it has only be studied for real floating point arithmetic. In this short note, we recall the known error-free transformations for real arithmetic and we propose some new error-free transformations for complex floating point arithmetic. This will make it possible to design some new accurate algorithms for summation, dot product and polynomial evaluation with complex entries.
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https://hal.archives-ouvertes.fr/hal-01306229
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Submitted on : Friday, April 22, 2016 - 3:42:06 PM
Last modification on : Thursday, March 21, 2019 - 1:19:17 PM

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  • HAL Id : hal-01306229, version 1

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Stef Graillat, Valérie Ménissier-Morain. Error-Free Transformations in Real and Complex Floating Point Arithmetic. International Symposium on Nonlinear Theory and its Applications (NOLTA'07), Sep 2007, Vancouver, Canada. pp.341-344. ⟨hal-01306229⟩

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