Scalings of matrices satisfying line-product constraints and generalizations
type: Item
instance of: scholarly article
title: Scalings of matrices satisfying line-product constraints and generalizations
zbMATH Open document ID: 0764.15005
DOI: 10.1016/0024-3795(92)90307-V
author: Uriel G. Rothblum
author: Stavros A. Zenios
published in: Linear Algebra and its Applications
publication date: 1993-01-16T00:00:00Z
review text: This paper develops equivalent least squares problems to find positive diagonal matrices \(D_ i\) such that the row products and column products in \(D_ 1AD_ 2\) are identical in value for a given nonnegative square matrix \(A\) and so that possibly \(D_ 1=D_ 2^{-1}\). The methods rely on graph theoretical matrix analysis and optimization techniques, analogues of which have been used earlier to solve the diagonal scaling problem for equal row and column sums and equal row and column maxima. An extensive outline of various scaling results is given as the introduction. The final section gives an algorithm each for diagonal and symmetric \((D_ 1=D_ 2^{-1})\) scaling with respect to equal row and column products.
reviewed by: Frank Uhlig
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 95481
zbMATH Keywords: least squares
zbMATH Keywords: positive diagonal matrices
zbMATH Keywords: optimization
zbMATH Keywords: diagonal scaling problem
zbMATH Keywords: algorithm
MaRDI profile type: Publication
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full work available at URL: 0024-3795(92)90307-v
OpenAlex ID: W2091467814
description: scientific article; zbMATH DE number 95481