On factorizations of smooth nonnegative matrix-values functions and on smooth functions with values in polyhedra

N. V. Krylov

doi:10.1007/s00245-008-9040-2

On factorizations of smooth nonnegative matrix-values functions and on smooth functions with values in polyhedra

N. V. Krylov

School of Mathematics

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

11 Scopus citations

Abstract

We discuss the possibility to represent smooth nonnegative matrix-valued functions as finite linear combinations of fixed matrices with positive real-valued coefficients whose square roots are Lipschitz continuous. This issue is reduced to a similar problem for smooth functions with values in a polyhedron.

Original language	English (US)
Pages (from-to)	373-392
Number of pages	20
Journal	Applied Mathematics and Optimization
Volume	58
Issue number	3
DOIs	https://doi.org/10.1007/s00245-008-9040-2
State	Published - Dec 2008

Bibliographical note

Funding Information:
The work was partially supported by NSF Grant DMS-0653121.

Keywords

Diagonally dominant matrices
Finite-difference approximations
Polyhedra

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10.1007/s00245-008-9040-2

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title = "On factorizations of smooth nonnegative matrix-values functions and on smooth functions with values in polyhedra",

abstract = "We discuss the possibility to represent smooth nonnegative matrix-valued functions as finite linear combinations of fixed matrices with positive real-valued coefficients whose square roots are Lipschitz continuous. This issue is reduced to a similar problem for smooth functions with values in a polyhedron.",

keywords = "Diagonally dominant matrices, Finite-difference approximations, Polyhedra",

author = "Krylov, {N. V.}",

note = "Funding Information: The work was partially supported by NSF Grant DMS-0653121.",

year = "2008",

month = dec,

doi = "10.1007/s00245-008-9040-2",

language = "English (US)",

volume = "58",

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journal = "Applied Mathematics and Optimization",

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AU - Krylov, N. V.

N1 - Funding Information: The work was partially supported by NSF Grant DMS-0653121.

PY - 2008/12

Y1 - 2008/12

N2 - We discuss the possibility to represent smooth nonnegative matrix-valued functions as finite linear combinations of fixed matrices with positive real-valued coefficients whose square roots are Lipschitz continuous. This issue is reduced to a similar problem for smooth functions with values in a polyhedron.

AB - We discuss the possibility to represent smooth nonnegative matrix-valued functions as finite linear combinations of fixed matrices with positive real-valued coefficients whose square roots are Lipschitz continuous. This issue is reduced to a similar problem for smooth functions with values in a polyhedron.

KW - Diagonally dominant matrices

KW - Finite-difference approximations

KW - Polyhedra

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JO - Applied Mathematics and Optimization

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ER -

On factorizations of smooth nonnegative matrix-values functions and on smooth functions with values in polyhedra

Abstract

Bibliographical note

Keywords

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