On constructing unit triangular matrices with prescribed singular values
type: Item
instance of: scholarly article
title: On constructing unit triangular matrices with prescribed singular values
zbMATH Open document ID: 0958.65045
author: Przemysław Kosowski
author: Alicja Smoktunowicz
published in: Computing
publication date: 2001-04-10T00:00:00Z
review text: The purpose of this paper is to provide an efficient algorithm for computing a unit lower triangular \(n\times n\) matrix with prescribed singular values \(\sigma_1,\dots, \sigma_n\), where \(\Pi_i\sigma_i= 1\). The idea of the proposed algorithm is to construct a sequence of unitarily equivalent lower triangular matrices \(A_i\in \mathbb{R}^{n\times n}\), \(i= 1,\dots, n\) with diagonal matrix \(\text{diag}(\sigma_1,\sigma_2,\dots, \sigma_n)\), where \(\sigma_1,\sigma_2,\dots, \sigma_n\), are given singular values. Numerical properties of the proposed algorithm depend mainly on the accuracy of the singular value decomposition routine for a \(2\times 2\) triangular matrix. All computations were carried out in MATLAB.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 1501441
zbMATH Keywords: stability
zbMATH Keywords: triangular matrix
zbMATH Keywords: computing
zbMATH Keywords: prescribed singular values
zbMATH Keywords: singular value decomposition
reviewed by: Florica Luban
describes a project that uses: mctoolbox
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: s006070050047
OpenAlex ID: W2046929266
DOI: 10.1007/S006070050047
description: scientific article; zbMATH DE number 1501441