Q889185
type: Item
instance of: scholarly article
title: Matrices of small Toeplitz rank, certain representations of the solution to an unstable system of linear equations with Toeplitz coefficient matrices, and related fast algorithms for solving such systems
zbMATH Open document ID: 1330.65062
DOI: 10.1134/S0965542514110050
author: V. I. Gel'fgat
published in: Computational Mathematics and Mathematical Physics
publication date: 2015-11-06T00:00:00Z
review text: The Toeplitz (cs)- and (sc)-decompositions are introduced and analysed for an arbitary square complex matrix based on their connections with solutions of two implicit Sylvester equations. Then, formulas for the solution of Tikhonov regularization problems are derived. These formulas show that the number of arithmetic operations required for solving a sequence of unstable problems is twice as large as the corresponding number for stable problems.
Mathematics Subject Classification ID: 65F22
zbMATH DE Number: 6505321
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: Toeplitz system
zbMATH Keywords: unstable system
zbMATH Keywords: fast algorithm
reviewed by: Liu Xinguo
MaRDI profile type: Publication
cites work: Q3706407
cites work: Q3776480
cites work: On certain decompositions of complex inverse Toeplitz matrices and related fast algorithms for solving linear systems with Toeplitz coefficient matrices
cites work: Q3700677
cites work: Q5691986
cites work: Q3735040
cites work: Shifted discrete Fourier transformations
label: Matrices of small Toeplitz rank, certain representations of the solution to an unstable system of linear equations with Toeplitz coefficient matrices, and related fast algorithms for solving such systems
description: scientific article; zbMATH DE number 6505321