Structure theory and fast inversion of Hankel striped matrices. I
type: Item
instance of: scholarly article
title: Structure theory and fast inversion of Hankel striped matrices. I
zbMATH Open document ID: 0711.15031
DOI: 10.1007/BF01272119
published in: Integral Equations and Operator Theory
publication date: 1988-01-01T00:00:00Z
review text: Hankel striped matrices are matrices of the form \(H=[H_ 1H_ 2...H_ r]\) where the \(H_ j\) are \(m\times n_ j\) Hankel matrices. A structure theory is developed for the kernel of a Hankel striped matrix. This theory is based on the consideration of the family of Hankel striped matrices \(H^{(k)}=[H_ 1^{(k)}H_ 2^{(k)}...H_ r^{(k)}]\) where \(H_ j^{(k)}\) is the \(k\times (m+n_ j-k)\) Hankel matrix determined by \(H_ j\). In particular, the partial indices (in the sense of another paper by the author [ibid. 8, 805-824 (1985; Zbl 0595.47015)]) are identified. Using this structure theory, fast algorithms are developed for inversion of Hankel striped matrices. The well-known Levinson-Trench algorithm appears as a very special case of these fast algorithms.
reviewed by: Leiba Rodman
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 47A65
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 4168868
zbMATH Keywords: Hankel striped matrices
zbMATH Keywords: Hankel matrices
zbMATH Keywords: structure theory
zbMATH Keywords: fast algorithms
zbMATH Keywords: inversion of Hankel striped matrices
zbMATH Keywords: Levinson-Trench algorithm
author: G. Heinig
MaRDI profile type: Publication
cites work: Q3316455
cites work: Algebraic methods for Toeplitz-like matrices and operators
cites work: On inversion of block Toeplitz matrices
cites work: Partial indices for Toeplitz-like operators
description: scientific article; zbMATH DE number 4168868