Enhanced Floating-Point Sums, Dot Products, and Polynomial Values

Jean-Michel Muller,Guillaume Melquiond,Serge Torres,Nathalie Revol,Nicolas Brisebarre,Claude-Pierre Jeannerod,Florent De Dinechin,Damien Stehlé,Vincent Lefèvre

doi:10.1007/978-0-8176-4705-6_6

Enhanced Floating-Point Sums, Dot Products, and Polynomial Values

Jean-Michel Muller, Guillaume Melquiond + Show 7 more

https://doi.org/10.1007/978-0-8176-4705-6_6

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Publication Date: Oct 30, 2009

Affiliation: École Normale Supérieure de Lyon, Macquarie University, University of Sydney

#Dot Products #Computation Of Sums + Show 6 more

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Abstract

AbstractIn this chapter, we focus on the computation of sums and dot products, and on the evaluation of polynomials in IEEE 754 floating-point arithmetic.1 Such calculations arise in many fields of numerical computing. Computing sums is required, e.g., in numerical integration and the computation of means and variances. Dot products appear everywhere in numerical linear algebra. Polynomials are used to approximate many functions (see Chapter 11).

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