Scalings of matrices satisfying line-product constraints and generalizations
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.
scientific article; zbMATH DE number 95481
scientific article