A Variational Equivalent to Diagonal Scaling.

Abstract

This paper is concerned with the problem of diagonally scaling a given nonnegative matrix a to one with prescribed row and column sums. The approach is to represent one of the two scaling matrices as the solution of a variational problem. This leads in a natural way to necessary and sufficient conditions on the zero pattern of a so that such a scaling exists. In addition the convergence of the successive prescribed row and column sum normalizations is established. Certain invariants under diagonal scaling are used to actually compute the desired scaled matrix, and examples are provided. Finally, at the end of the paper, a discussion of infinite systems is presented. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1978
Accession Number
ADA054548

Entities

People

  • Carl Timothy Kelley
  • Marc A. Berger

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Banach Space
  • Convergence
  • Convex Sets
  • Equations
  • Functional Analysis
  • Hilbert Space
  • Inequalities
  • Information Theory
  • Linear Algebra
  • Mathematics
  • Military Research
  • New York
  • North Carolina
  • Sequences
  • Theorems
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Linear Algebra