Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices. II: Algorithms
type: Item
instance of: scholarly article
title: Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices. II: Algorithms
zbMATH Open document ID: 0939.65039
DOI: 10.1016/S0024-3795(97)10043-X
author: G. Heinig
author: Adam W. Bojanczyk
published in: Linear Algebra and its Applications
publication date: 2000-06-19T00:00:00Z
review text: In continuation of the authors' earlier paper [part I, ibid. 254, 193-226 (1997; Zbl 0872.65021)] fast algorithms for LU-factorization and inversion of generalized Cauchy matrices are discussed. Cauchy matrices have the property that permutations of columns and rows preserve the Cauchy structure. This property provides additional freedom in how matrix decomposition algorithms based on Gaussian elimination can be applied. It turns out that instead of dealing with Toeplitz and Toeplitz-plus-Hankel matrices, it is worthwhile, from the numerical point of view, to deal with the corresponding Cauchy matrices. It is shown that the combination of transformation pivoting techniques leads to faster algorithms for infinite Toeplitz and Toeplitz-plus-Hankel matrices that are more stable than the classical ones.
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 1354769
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: Cauchy matrix
zbMATH Keywords: fast algorithm
zbMATH Keywords: matrix inversion
zbMATH Keywords: infinite matrices
zbMATH Keywords: LU-factorization
zbMATH Keywords: Gaussian elimination
zbMATH Keywords: Toeplitz-plus-Hankel matrices
zbMATH Keywords: pivoting techniques
reviewed by: Horst Hollatz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1354769