Numerical evaluation of the \(p\)th derivative of Jacobi series
type: Item
instance of: scholarly article
title: Numerical evaluation of the \(p\)th derivative of Jacobi series
zbMATH Open document ID: 1018.65031
DOI: 10.1016/S0168-9274(02)00106-X
author: Roberto Barrio
author: J. M. Peña
published in: Applied Numerical Mathematics
publication date: 2003-03-10T00:00:00Z
review text: An algorithm for the evaluation of the \(p\)th derivative at a given point of a polynomial expressed as a finite series of Jacobi polynomials is established. The algorithm permits the direct evaluation without obtaining the \(p\)th derivative of the polynomial itself, resulting in memory and time savings. Another algorithm for reducing the rounding errors near the end points of the interal of evaluation is given. The results established can be applied to various particular cases of Jacobi polynomials such as ultraspherical, Legendre and Chebyshev polynomials.
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33F05
zbMATH DE Number: 1879034
zbMATH Keywords: derivative evaluation
zbMATH Keywords: rounding errors
zbMATH Keywords: pseudospectral methods
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: ultraspherical polynomial
zbMATH Keywords: Legendre polynomial
zbMATH Keywords: algorithm
reviewed by: C. L. Koul
describes a project that uses: splib
describes a project that uses: mctoolbox
describes a project that uses: Differentiation Matrix Suite
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1879034