A Variational Equivalent to Diagonal Scaling

A Variational Equivalent to Diagonal Scaling

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 condi...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Berger,Marc A, Kelley,C T
Format: Report
Sprache:eng
Schlagworte:
INEQUALITIES
INVARIANCE
MATRIX THEORY
SEQUENCES(MATHEMATICS)
Theoretical Mathematics
TRANSFORMATIONS(MATHEMATICS)
VARIATIONAL METHODS
WEAK CONVERGENCE
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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)