Immittance- versus scattering-domain fast algorithms for non-Hermitian Toeplitz and quasi-Toeplitz matrices
type: Item
instance of: scholarly article
title: Immittance- versus scattering-domain fast algorithms for non-Hermitian Toeplitz and quasi-Toeplitz matrices
zbMATH Open document ID: 0693.65018
DOI: 10.1016/0024-3795(89)90678-2
author: Hanoch Lev-Ari
author: Yuval Bistritz
author: T. Kailath
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: The classical algorithms of Schur and Levinson for solving or factoring a Hermitian Toeplitz matrix are considered here (as scattering-domain algorithms). Based on a recent carefully study of the authors on immittance-domain Schur and Levinson algorithms, this paper presents immittance versions of these algorithms for non-Hermitian Toeplitz and quasi-Toeplitz matrices. A study of all possible pairs of recursions of highest efficiency is presented, showing five essentially different pairs of recursions of equal efficiency. For the algorithms of Schur and Levinson, the immittance versions are presented in all five cases. It is also shown how the extended QT algorithm can also be transformed into immittance algorithm. The immittance version of each algorithm for non-Hermitian matrices needs as much computation as its scattering counterpart. Both the immittance and the scattering algorithms exploit the (quasi-) Toeplitz structure for producing fast algorithms. However, unlike the scattering algorithms, the immittance algorithms can utilize the symmetrical property of the matrix and in Hermitian cases produce algorithms of improved efficiency.
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 4135297
zbMATH Keywords: Levinson algorithm
zbMATH Keywords: Schur algorithm
zbMATH Keywords: scattering-domain algorithms
zbMATH Keywords: non- Hermitian Toeplitz and quasi-Toeplitz matrices
zbMATH Keywords: recursions
zbMATH Keywords: QT algorithm
zbMATH Keywords: immittance algorithm
zbMATH Keywords: efficiency
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90678-2
OpenAlex ID: W2013974402
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description: scientific article; zbMATH DE number 4135297