Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations
type: Item
instance of: scholarly article
title: Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations
zbMATH Open document ID: 0932.65025
DOI: 10.1016/S0377-0427(97)00157-X
author: Marlis Hochbruck
published in: Journal of Computational and Applied Mathematics
publication date: 1998-08-30T00:00:00Z
review text: The look-ahead algorithm of \textit{M. H. Gutknecht} and \textit{M. Hochbruck} [BIT 36, No. 2, 264-286 (1996; Zbl 0852.65025)] for computing the \((0,N)\) Padé form of a formal Laurent series with complex coefficients is improved. Two versions (Levinson-type and Schur-type) of the algorithm are considered. When the algorithms are used to solve Toeplitz systems of linear equations then the block LDU decompositions of the system matrix and its inverse can be found with less computational effort compared with other existing look-ahead algorithms. The main features of the algorithm are that it performs look-ahead steps of minimum size and that it reduces to the classical Levinson or Schur algorithm if only regular steps of size 1 are performed.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 1115934
zbMATH Keywords: Padé table
zbMATH Keywords: Levinson algorithm
zbMATH Keywords: look-ahead algorithm
zbMATH Keywords: formal Laurent series
zbMATH Keywords: Toeplitz systems
zbMATH Keywords: block LDU decompositions
zbMATH Keywords: Schur algorithm
Wikidata QID: Q114121039
reviewed by: Mihail M. Konstantinov
MaRDI profile type: Publication
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full work available at URL: s0377-0427(97)00157-x
OpenAlex ID: W2044738423
description: scientific article; zbMATH DE number 1115934