Linear rational finite differences from derivatives of barycentric rational interpolants

Klein, Georges; Berrut, Jean-Paul

doi:10.1137/110827156

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Journal article

Linear rational finite differences from derivatives of barycentric rational interpolants

Klein, Georges Department of Mathematics, University of Fribourg, Switzerland
Berrut, Jean-Paul Department of Mathematics, University of Fribourg, Switzerland

04.04.2012

Published in:

SIAM Journal on Numerical Analysis. - 2012, vol. 50, no. 2, p. 643–656

English Derivatives of polynomial interpolants lead in a natural way to approximations of derivatives of the interpolated function, e.g., through finite differences. We extend a study of the approximation of derivatives of linear barycentric rational interpolants and present improved finite difference formulas arising from these interpolants. The formulas contain the classical finite differences as a special case and are more stable for calculating one-sided derivatives as well as derivatives close to boundaries.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language