Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic

Abstract : Several different techniques and softwares intend to improve the accuracy of results computed in a fixed finite precision. Here we focus on methods to improve the accuracy of summation, dot product and polynomial evaluation. Such algorithms exist real floating point numbers. In this paper, we provide new algorithms which deal with complex floating point numbers. We show that the computed results are as accurate as if computed in twice the working precision. The algorithms are simple since they only require addition subtraction and multiplication of floating point numbers in the same working precision as the given data.
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https://hal.archives-ouvertes.fr/hal-01146509
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Submitted on : Tuesday, April 28, 2015 - 2:46:11 PM
Last modification on : Thursday, March 21, 2019 - 2:37:58 PM

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Stef Graillat, Valérie Ménissier-Morain. Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic. Information and Computation, Elsevier, 2012, pp.57-71. ⟨10.1016/j.ic.2011.09.003⟩. ⟨hal-01146509⟩

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