Sine transform based preconditioners for symmetric Toeplitz systems
type: Item
instance of: scholarly article
title: Sine transform based preconditioners for symmetric Toeplitz systems
zbMATH Open document ID: 0837.65043
DOI: 10.1016/0024-3795(94)00049-2
author: Yanyan Li
published in: Linear Algebra and its Applications
publication date: 1996-05-21T00:00:00Z
review text: The authors construct an optimal sine transform based preconditioner which is defined to be the minimizer of \(|B- A|_F\) over the set of matrices \(B\) that can be diagonalized by sine transforms. They prove that for general \(n\)-by-\(n\) matrices \(A\), these optimal preconditioners can be constructed in \(O(n^2)\) real operations and in \(O(n)\) real operations if \(A\) is Toeplitz. They also show that the convergence properties of these optimal sine transform preconditioners are the same as that of the optimal circulant ones when they are employed to solve Toeplitz systems. Numerical examples are given to illustrate the convergence analysis.
reviewed by: F. Szidarovszky
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15A12
zbMATH DE Number: 841763
zbMATH Keywords: numerical examples
zbMATH Keywords: sine transform
zbMATH Keywords: optimal preconditioners
zbMATH Keywords: convergence
zbMATH Keywords: Toeplitz systems
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00049-2
OpenAlex ID: W2070661544
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description: scientific article; zbMATH DE number 841763