Split algorithms for skewsymmetric Toeplitz matrices with arbitrary rank profile
type: Item
instance of: scholarly article
title: Split algorithms for skewsymmetric Toeplitz matrices with arbitrary rank profile
zbMATH Open document ID: 1060.65033
author: G. Heinig
author: Karla Rost
published in: Theoretical Computer Science
publication date: 2004-08-06T00:00:00Z
review text: A skewsymmetric Toeplitz matrix has the form \(T_N=[a_{i-j}]_{i,j=1}^N\) with \(a_{-j}=-a_j\). A general linear system \(T_Nf=b\) with a nonsingular Toeplitz matrix can be solved `fast' with complexity \(O(n^2)\) using Levinson-type or Schur-type algorithms. However, these require that all leading principal submatrices are nonsingular which rules out all skewsymmetric Toeplitz matrices. In a previous paper [Oper. Theory Adv. Appl. 135, 193--208 (2002; Zbl 1022.65028)] the authors obtained a fast algorithm for the case of centro-nonsingular matrices. In the present paper they generalize this to all nonsingular skewsymmetric Toeplitz matrices. Their algorithm is related to generalizations of \(ZW\) and \(WZ\) factorizations of matrices.
reviewed by: Willy J. F. Govaerts
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 2083139
zbMATH Keywords: \(ZW\) factorization
zbMATH Keywords: skewsymmetric Toeplitz matrix
zbMATH Keywords: split algorithm
zbMATH Keywords: Levinson algorithm
zbMATH Keywords: Schur algorithm
zbMATH Keywords: \(WZ\)-factorization
MaRDI profile type: Publication
full work available at URL: j.tcs.2004.01.003
OpenAlex ID: W2077222805
cites work: Q4314299
cites work: Error analysis of algorithms for matrix multiplication and triangular decomposition using Winograd's identity
cites work: A parallel linear system solver
cites work: Q3683414
cites work: Chebyshev-Hankel matrices and the splitting approach for centrosymmetric Toeplitz-plus-Hankel matrices
cites work: Algebraic methods for Toeplitz-like matrices and operators
cites work: DFT representations of Toeplitz-plus-Hankel Bézoutians with application to fast matrix-vector multiplication
cites work: Efficient inversion formulas for Toeplitz-plus-Hankel matrices using trigonometric transformations
cites work: Centro-symmetric and centro-skewsymmetric Toeplitz matrices and Bézoutians
cites work: Q4801260
cites work: Split algorithms for symmetric Toeplitz matrices with arbitrary rank profile
cites work: A two-step even-odd split Levinson algorithm for Toeplitz systems
cites work: Q2760974
cites work: Existence and uniqueness of WZ factorization
cites work: Q3776480
DOI: 10.1016/J.TCS.2004.01.003
Recommended article: Split algorithms for symmetric Toeplitz matrices with arbitrary rank profile
Recommended article: Split algorithms for Hermitian Toeplitz matrices with arbitrary rank profile
Recommended article: Q3434426
Recommended article: Q5313649
Recommended article: New analogs of split algorithms for arbitrary Toeplitz-plus-Hankel matrices
Recommended article: Q4801260
Recommended article: Q5481361
Recommended article: The Shifted Classical Circulant and Skew Circulant Splitting Iterative Methods for Toeplitz Matrices
Recommended article: A symmetric rank-revealing toeplitz matrix decomposition
Recommended article: On the preconditioning of matrices with skew-symmetric splittings
description: scientific article; zbMATH DE number 2083139