Stochastic Galerkin Matrices

Authors:
Oliver G. Ernst;Elisabeth Ullmann
Affiliations:
ernst@math.tu-freiberg.de and ullmann@math.tu-freiberg.de;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2010

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Abstract

We investigate the structural, spectral, and sparsity properties of Stochastic Galerkin matrices as they arise in the discretization of linear differential equations with random coefficient functions. These matrices are characterized as the Galerkin representation of polynomial multiplication operators. In particular, it is shown that the global Galerkin matrix associated with complete polynomials cannot be diagonalized in the stochastically linear case.