Customizable triangular factorizations of matrices
type: Item
instance of: scholarly article
title: Customizable triangular factorizations of matrices
zbMATH Open document ID: 1050.15012
author: Pengwei Hao
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: The author obtains a number of matrix factorizations, where some of the factors are customized. Here `customized' means having special entries which are particularly well suited for some applications, or allowing fast numerical calculations. A typical result in the paper is the following: Given the customized diagonal entries of an upper triangular matrix \(U\) as \(d_1,d_2,\ldots,d_N\), an \(N\times N\) matrix \(A\) has a PLUS factorization \(A= \text{PLUS}\) if and only if \(\det A=\pm d_1d_2\cdots d_N\neq0\), where \(P\) is a permutation or an upper pseudo-permutation matrix, \(L\) is a unit lower triangular matrix, \(S\) is a unit single-row matrix with \(N-1\) elements in the customized positions of \(S(N,k)\) for \(k=1,2,3,\ldots,N-1\), or \(S=I+e_Ns_N^T\).
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 2081905
zbMATH Keywords: triangular matrix
zbMATH Keywords: triangular factorization
zbMATH Keywords: reversible integer transform
zbMATH Keywords: rotation by shears
Wikidata QID: Q114152476
MaRDI profile type: Publication
full work available at URL: j.laa.2003.12.023
OpenAlex ID: W2128298390
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DOI: 10.1016/J.LAA.2003.12.023
description: scientific article; zbMATH DE number 2081905