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BIT Numerical Mathematics

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01-12-2015

The multivariate Horner scheme revisited

Authors: Johannes Czekansky, Tomas Sauer

Published in: BIT Numerical Mathematics | Issue 4/2015

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Abstract

We compare two variants of a multivariate Horner scheme for polynomials of a certain total degree with respect to computational effort and backward error.

previous article A posteriori error analysis for finite element methods with projection operators as applied to explicit time integration techniques

next article Weak backward error analysis for Langevin process

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Reference: Intel i5 @ 2.7 Ghz, GNU Octave, version 3.4.0.

de Boor, C.: Computational aspects of multivariate polynomial interpolation: indexing the coefficients. Adv. Comput. Math. 12(4), 289–301 (2000)CrossRefMathSciNetMATH

Higham, N.: Accuracy and Stability of Numerical Algorithms, 2nd edn. SIAM (2002)

Peña, J., Sauer, T.: On the multivariate Horner scheme. SIAM J. Numer. Anal. 37, 1186–1197 (2000)CrossRefMathSciNetMATH

Peña, J.M., Sauer, T.: On the multivariate Horner scheme II: running error analysis. Computing 65, 313–322 (2000)CrossRefMathSciNetMATH

Sauer, T.: Computational aspects of multivariate polynomial interpolation. Adv. Comput. Math. 3, 219–238 (1995)

Schumaker, L.L., Volk, W.: Efficient evaluation of multivariate polynomials. Comput. Aided Geom. Design 3, 149–154 (1986)CrossRefMATH

Title: The multivariate Horner scheme revisited
Authors: Johannes Czekansky
Tomas Sauer
Publication date: 01-12-2015
Publisher: Springer Netherlands
Published in: BIT Numerical Mathematics / Issue 4/2015
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-014-0533-x

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