Symmetric Gaussian elimination for Cauchy-type matrices with application to positive definite Toeplitz matrices
type: Item
instance of: scholarly article
title: Symmetric Gaussian elimination for Cauchy-type matrices with application to positive definite Toeplitz matrices
zbMATH Open document ID: 0913.65019
published in: Numerische Mathematik
publication date: 1999-05-25T00:00:00Z
review text: New methods for solving systems of linear equations with Hermitian positive definite Toeplitz matrices are given. The given matrix is first transformed into a Cauchy-type matrix, then symmetric Gaussian elimination is applied. For moderately ill-conditioned matrices total pivoting is proposed. For very ill-conditioned matrices an alternative method is described. This involves the replacement of small diagonal entries by a small number. The total computational cost is \(O(n^2)\). It is shown by computational experiments that the proposed algorithms are stable and reliable. Relative advantages of the author's methods over other known methods are carefully documented.
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 1180712
zbMATH Keywords: Gaussian elimination
zbMATH Keywords: Toeplitz matrices
zbMATH Keywords: Cauchy-type matrices
zbMATH Keywords: numerical examples
zbMATH Keywords: ill-conditioned matrices
zbMATH Keywords: algorithms
author: Thomas K. Huckle
reviewed by: R. P. Tewarson
MaRDI profile type: Publication
full work available at URL: s002110050338
OpenAlex ID: W2073613476
DOI: 10.1007/S002110050338
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description: scientific article; zbMATH DE number 1180712