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

Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol and Serge Torres
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Jean-Michel Muller: CNRS - LIP
Nicolas Brunie: Kalray
Florent de Dinechin: INSA-Lyon - CITI
Claude-Pierre Jeannerod: Inria - LIP
Mioara Joldes: CNRS - LAAS
Vincent Lefèvre: Inria - LIP
Guillaume Melquiond: Inria - LRI
Nathalie Revol: Inria - LIP
Serge Torres: ENS-Lyon - LIP

Chapter Chapter 5 in Handbook of Floating-Point Arithmetic, 2018, pp 163-192 from Springer

Abstract: Abstract In this chapter, we focus on the computation of sums and dot products, and on the evaluation of polynomials in IEEE 754 floating-point arithmetic. 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 10 ).

Date: 2018
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DOI: 10.1007/978-3-319-76526-6_5

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