Stochastic galerkin matrices

Oliver G. Ernst; Elisabeth Ullmann

doi:10.1137/080742282

Stochastic galerkin matrices

Oliver G. Ernst, Elisabeth Ullmann

Technische Universität Bergakademie Freiberg

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

56 Scopus citations

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.

Original language	English
Pages (from-to)	1848-1872
Number of pages	25
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	31
Issue number	4
DOIs	https://doi.org/10.1137/080742282
State	Published - 2009
Externally published	Yes

Keywords

Orthogonal polynomials
Stochastic Galerkin method
Stochastic finite elements

Access to Document

10.1137/080742282

Cite this

@article{abb751ecdd0d46abb4b33803079f9127,

title = "Stochastic galerkin matrices",

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.",

keywords = "Orthogonal polynomials, Stochastic Galerkin method, Stochastic finite elements",

author = "Ernst, {Oliver G.} and Elisabeth Ullmann",

year = "2009",

doi = "10.1137/080742282",

language = "English",

volume = "31",

pages = "1848--1872",

journal = "SIAM Journal on Matrix Analysis and Applications",

issn = "0895-4798",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "4",

}

TY - JOUR

T1 - Stochastic galerkin matrices

AU - Ernst, Oliver G.

AU - Ullmann, Elisabeth

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Orthogonal polynomials

KW - Stochastic Galerkin method

KW - Stochastic finite elements

UR - http://www.scopus.com/inward/record.url?scp=77956039499&partnerID=8YFLogxK

U2 - 10.1137/080742282

DO - 10.1137/080742282

M3 - Article

AN - SCOPUS:77956039499

SN - 0895-4798

VL - 31

SP - 1848

EP - 1872

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 4

ER -

Stochastic galerkin matrices

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this