Stabilizing Trench's algorithm to invert symmetric Toeplitz matrices
type: Item
instance of: scholarly article
title: Stabilizing Trench's algorithm to invert symmetric Toeplitz matrices
zbMATH Open document ID: 0794.65018
DOI: 10.1016/0096-3003(94)90108-2
published in: Applied Mathematics and Computation
publication date: 1994-08-31T00:00:00Z
review text: The original Trench algorithm for the inversion of Toeplitz matrices may be applied only to matrices with non-vanishing leading minors. When leading minors of the Toeplitz matrix \(T\) are vanishing or nearly vanishing, the authors propose to apply \textit{S. Zohar's} formulation of Trench's algorithm [J. Assoc. Comput. Machin. 16, 592-601 (1969; Zbl 0194.181) and ibid. 21, 272-276 (1974; Zbl 0276.65014)] to the positive definite \(T+\alpha I\) and to use persymmetric diagonal modifications of this matrix to evaluate \(T^{-1}\). The efficiency of the algorithm is achieved by careful exploitation of the symmetry and persymmetry properties of the matrices involved in computations.
reviewed by: Z. Dostál
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 519659
zbMATH Keywords: matrix inversion
zbMATH Keywords: Trench's algorithm
zbMATH Keywords: inversion of Toeplitz matrices
author: V. Lakshmikantham
author: Syamal K. Sen
author: V. Ch. Venkaiah
author: Seenith Sivasundaram
MaRDI profile type: Publication
full work available at URL: 0096-3003(94)90108-2
OpenAlex ID: W2122929512
cites work: Stability of Methods for Solving Toeplitz Systems of Equations
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cites work: Q4057472
cites work: An Algorithm for the Inversion of Finite Toeplitz Matrices
cites work: Toeplitz Matrix Inversion: The Algorithm of W. F. Trench
cites work: The Solution of a Toeplitz Set of Linear Equations
description: scientific article; zbMATH DE number 519659