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

doi:10.1137/S0895479895293247

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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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 ℓ_p vector norm for any p.

Original language	English (US)
Pages (from-to)	249-257
Number of pages	9
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	18
Issue number	1
DOIs	https://doi.org/10.1137/S0895479895293247
State	Published - Jan 1997

Keywords

Nonnegative matrices
Structured singular values
Volumetric singular values
Weighted l norms

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10.1137/S0895479895293247

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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.",

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AU - Huang, Wenchao

AU - Schneider, Hans

AU - Weinberger, Hans

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N2 - 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.

AB - 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.

KW - Nonnegative matrices

KW - Structured singular values

KW - Volumetric singular values

KW - Weighted l norms

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JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

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ER -

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

Abstract

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