Applied Mathematics and Optimization

, Volume 58, Issue 3, pp 373–392

On Factorizations of Smooth Nonnegative Matrix-Values Functions and on Smooth Functions with Values in Polyhedra


DOI: 10.1007/s00245-008-9040-2

Cite this article as:
Krylov, N.V. Appl Math Optim (2008) 58: 373. doi:10.1007/s00245-008-9040-2


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.


Finite-difference approximationsPolyhedraDiagonally dominant matrices

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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.University of MinnesotaMinneapolisUSA