DFT representations of Toeplitz-plus-Hankel Bézoutians with application to fast matrix-vector multiplication
type: Item
instance of: scholarly article
title: DFT representations of Toeplitz-plus-Hankel Bézoutians with application to fast matrix-vector multiplication
zbMATH Open document ID: 0938.65073
DOI: 10.1016/S0024-3795(98)10076-9
author: G. Heinig
author: Karla Rost
published in: Linear Algebra and its Applications
publication date: 1999-11-28T00:00:00Z
review text: The authors discuss possibilities of fast matrix-vector multiplication by inverse Toeplitz-plus-Hankel matrices. The approach is based on the following two facts: Inverses of Toeplitz-plus-Hankel matrices are Toeplitz-plus-Hankel Bézoutians and these can be transformed into Cauchy-like matrices. Then, these Cauchy-like matrices can be represented by using discrete Fourier transforms (DFT's). The authors show how Bézoutians can be transformed into Cauchy matrices with the help of Vandermonde matrices, in particular DFT's. Using these properties, one can perform a matrix-vector multiplication by an inverse Toeplitz-plus-Hankel matrix with six DFT's and eight DFT's for preprocessing. This are fewer DFT's than in the so far best known algorithm with seven DFT's plus 10 DFT's for preprocessing [see \textit{E. Bozzo}, Linear Algebra Appl. 230, 127-150 (1995; Zbl 0839.15007)].
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 1371014
zbMATH Keywords: fast matrix-vector multiplication
zbMATH Keywords: inverse Toeplitz-plus-Hankel matrices
zbMATH Keywords: Bézoutian
zbMATH Keywords: Cauchy-like matrices
zbMATH Keywords: discrete Fourier transform
zbMATH Keywords: fast algorithm
zbMATH Keywords: Vandermonde matrices
reviewed by: Michael Jung
describes a project that uses: mctoolbox
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1371014