Backward stability of Clenshaw's algorithm
type: Item
instance of: scholarly article
title: Backward stability of Clenshaw's algorithm
zbMATH Open document ID: 1019.65004
DOI: 10.1023/A:1022001931526
author: Alicja Smoktunowicz
published in: BIT
publication date: 2003-05-14T00:00:00Z
review text: The question of the effect of roundoff errors in applying \textit{C. W. Clenshaw}'s algorithm [A note on the summation of Chebyshev series. Math. Tables Aids Comput. 9, 118-120 (1955; Zbl 0065.05403)] for summing the series \(w=b_0p_0+b_1p_1+ \ldots +b_np_n\) where \(p_n\) satisfy the linear three-term recurrence relation has been studies. The author gives some sufficient conditions under which Clenshaw's algorithm is backward stable. And finally, he proves that under certain assumptions, Clenshaw's algorithm is backward stable with respect to the data \(b_n\), \(n=0,1 \dots,N.\)
Mathematics Subject Classification ID: 65B10
Mathematics Subject Classification ID: 65G50
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1886392
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: numerical stability
zbMATH Keywords: series summation
zbMATH Keywords: roundoff errors
zbMATH Keywords: Clenshaw's algorithm
reviewed by: Antonio López-Carmona
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1886392