Interval-constrained matrix balancing
type: Item
instance of: scholarly article
title: Interval-constrained matrix balancing
zbMATH Open document ID: 0724.65043
DOI: 10.1016/0024-3795(91)90182-V
author: Yair Censor
author: Stavros A. Zenios
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: The following two problems are studied: 1. Given a nonnegative (m,n)-matrix \(A=(a_{ij})\) and positive vectors u, v; determine a `nearby' nonnegative (m,n)-matrix \(X=(x_{ij})\) such that \(\sum_{j}x_{ij}=u_ i\), \(i=1,...,m\), \(\sum_{i}x_{ij}=v_ j\), \(j=1,...,n\) and \(x_{ij}>0\) only if \(a_{ij}>0.\) 2. Given the same matrix as above \((m=n)\); find a `nearby' nonnegative matrix X such that \(\sum_{j}x_{ij}=\sum_{j}x_{ji}\), \(i=1,...,n\) and \(x_{ij}>0\) only if \(a_{ij}>0.\) It is considered the entropy optimization approach to define the `nearness' in these problems. A numerical method for solving is given. Numerical experiments illustrate the efficiency and effectiveness of the method and its superior performance when implemented in parallel.
reviewed by: Horst Hollatz
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 15A12
zbMATH DE Number: 4195048
zbMATH Keywords: interval-constrained matrix balancing
zbMATH Keywords: parallel algorithm
zbMATH Keywords: nonnegative matrix
zbMATH Keywords: entropy optimization
zbMATH Keywords: Numerical experiments
MaRDI profile type: Publication
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full work available at URL: 0024-3795(91)90182-v
OpenAlex ID: W2028155257
description: scientific article; zbMATH DE number 4195048