A fast algorithm for solving a Toeplitz system
type: Item
instance of: scholarly article
title: A fast algorithm for solving a Toeplitz system
zbMATH Open document ID: 1298.65050
author: Xiangjian Xu
published in: Applied Mathematics and Computation
publication date: 2010-11-18T00:00:00Z
review text: The author derives a fast algorithm for solving symmetric penta-diagonal systems. The Toeplitz \(n \times n\) matrix \(A\) of the system of linear algebraic equations is decomposed. The Sherman-Morison-Woodbury formula is used to obtain conditions under which the matrix \(A\) is invertible. Quite complicated formulas lead to a fast algorithm for solving the original system. The author proves that for strictly diagonally dominant \(A\) the algorithm is stable and works well. Two numerical examples illustrate the theory.
reviewed by: Drahoslava Janovská
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 15B05
zbMATH DE Number: 5817279
zbMATH Keywords: symmetric penta-diagonal systems of linear algebraic equations
zbMATH Keywords: fast direct algorithm for finding a solution
zbMATH Keywords: stability analysis
zbMATH Keywords: Toeplitz system
zbMATH Keywords: diagonally dominant
zbMATH Keywords: factorization
MaRDI profile type: Publication
full work available at URL: j.amc.2010.06.050
OpenAlex ID: W2016398512
cites work: A fast algorithm for solving Toeplitz penta-diagonal systems
cites work: Q3640433
cites work: Parallel algorithms for solving tridiagonal and near-circulant systems.
DOI: 10.1016/J.AMC.2010.06.050
description: scientific article; zbMATH DE number 5817279