Approximability by weighted norms of the structured and volumetric singular values of a class of nonnegative matrices

Daniel Hershkowitz, Wenchao Huang, Hans Schneider, Hans Weinberger

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

A known result about the spectral radius of an irreducible nonnegative matrix is extended to all nonnegative matrices. By means of this result, it is shown that the structured singular value and the volumetric singular value of a class of nonnegative matrices can be approximated with arbitrary accuracy by the matrix norm induced by a weighted ℓ2 vector norm and in the simplest case by a weighted ℓp vector norm for any p.

Original languageEnglish (US)
Pages (from-to)249-257
Number of pages9
JournalSIAM Journal on Matrix Analysis and Applications
Volume18
Issue number1
DOIs
StatePublished - Jan 1997

Keywords

  • Nonnegative matrices
  • Structured singular values
  • Volumetric singular values
  • Weighted l norms

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