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

2007/06/01 by N. V. Krylov, Krylov, N. V.
Mathematics · #15A99 #65M06 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #math.AP #math.OC #msc:15A99 #msc:65M06

paper · pdf · doi:10.48550/arxiv.0706.0192

19 pages

arxiv created 2007/06/01 · arxiv updated 2009/12/01

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.

Related

• Convex Algorithms for Nonnegative Matrix Factorization
• Continuous analogues of matrix factorizations
• Computing approximate PSD factorizations
• Factorization of piecewise constant matrix functions and systems of linear differential equations
• Integer factorization of a positive-definite matrix