Fast triangular factorization of the sum of quasi-Toeplitz and quasi- Hankel matrices
type: Item
instance of: scholarly article
title: Fast triangular factorization of the sum of quasi-Toeplitz and quasi- Hankel matrices
zbMATH Open document ID: 0784.65020
DOI: 10.1016/0024-3795(93)90510-U
author: Ali H. Sayed
author: Hanoch Lev-Ari
author: T. Kailath
published in: Linear Algebra and its Applications
publication date: 1993-12-12T00:00:00Z
review text: The paper presents fast triangular factorization algorithms \([O(n^ 2)]\) for matrices close to Toeplitz plus Hankel, and in particular for quasi- Toeplitz, quasi-Hankel, and Toeplitz-plus-Hankel matrices. Both Hermitian and non-Hermitian matrices are considered. Quasi-Toeplitz and quasi- Hankel matrices are those that are congruent to Toeplitz and Hankel matrices in a special sense. The derivation is based on the concept of displacement structure and its close relation to the Schur reduction for triangular factorization. It is an extension from the Hermitian case presented by the second and third author [Oper. Theory Adv. Appl. 18, 301-324 (1986; Zbl 0593.47015)] to the non-Hermitian case of the generating function approach inclusive structured non-Hermitian matrices. Various special cases covering displacement rank from two to eight are considered. The result includes many special cases studied separately, for instance factorization of the inverse matrix, solution of exact and overdetermined linear systems which can be reduced to the direct factorization problem.
reviewed by: Lubomír Bakule
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 459077
zbMATH Keywords: quasi-Toeplitz matrices
zbMATH Keywords: quasi-Hankel matrices
zbMATH Keywords: fast triangular factorization algorithms
zbMATH Keywords: Toeplitz-plus-Hankel matrices
zbMATH Keywords: Hermitian matrices
zbMATH Keywords: displacement rank
zbMATH Keywords: instance factorization
zbMATH Keywords: inverse matrix
zbMATH Keywords: overdetermined linear systems
zbMATH Keywords: non-Hermitian matrices
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 459077