Improved error bounds for floating-point products and Horner's scheme

DOI10.1007/s10543-015-0555-zzbMath1342.65122OpenAlexW2042386348MaRDI QIDQ285288

Florian Bünger, Claude-Pierre Jeannerod, Siegfried Michael Rump

Publication date: 19 May 2016

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/hal-01137652/file/products.pdf

zbMATH Keywords

finite product of real numbersfloating-point productHorner's schemeIEEE 754 standardWilkinson-type error estimates

Mathematics Subject Classification ID

Roundoff error (65G50) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical computation of roots of polynomial equations (65H04)

Related Items (3)

Formally-verified round-off error analysis of Runge-Kutta methods ⋮ Sharp estimates for perturbation errors in summations ⋮ Numerical validation of compensated algorithms with stochastic arithmetic

Uses Software

• Matlab
• mctoolbox

Cites Work

• Unnamed Item
• On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic
• Improved Error Bounds for Inner Products in Floating-Point Arithmetic
• Improved Backward Error Bounds for LU and Cholesky Factorizations
• Accuracy and Stability of Numerical Algorithms
• Accurate Floating-Point Summation Part I: Faithful Rounding

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