Stochastic galerkin matrices

Oliver G. Ernst, Elisabeth Ullmann

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


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.

Original languageEnglish
Pages (from-to)1848-1872
Number of pages25
JournalSIAM Journal on Matrix Analysis and Applications
Issue number4
StatePublished - 2009
Externally publishedYes


  • Orthogonal polynomials
  • Stochastic Galerkin method
  • Stochastic finite elements


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