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Application of hierarchical matrices for computing the Karhunen–Loève expansion

Khoromskij, B. N. ; Litvinenko, A. ; Matthies, H. G.

Computing, 2009-04, Vol.84 (1-2), p.49-67 [Periódico revisado por pares]

Vienna: Springer Vienna

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Título:
Application of hierarchical matrices for computing the Karhunen–Loève expansion
Autor: Khoromskij, B. N. ; Litvinenko, A. ; Matthies, H. G.
Assuntos: Approximation ; Artificial Intelligence ; Boundary conditions ; Computer Appl. in Administrative Data Processing ; Computer Communication Networks ; Computer Science ; Differential equations ; Eigenvalues ; Information Systems Applications (incl.Internet) ; Integral equations ; Mathematical models ; Numerical analysis ; Partial differential equations ; Probability ; Random variables ; Software Engineering ; Stochastic models ; Studies
É parte de: Computing, 2009-04, Vol.84 (1-2), p.49-67
Notas: ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
Descrição: Realistic mathematical models of physical processes contain uncertainties. These models are often described by stochastic differential equations (SDEs) or stochastic partial differential equations (SPDEs) with multiplicative noise. The uncertainties in the right-hand side or the coefficients are represented as random fields. To solve a given SPDE numerically one has to discretise the deterministic operator as well as the stochastic fields. The total dimension of the SPDE is the product of the dimensions of the deterministic part and the stochastic part. To approximate random fields with as few random variables as possible, but still retaining the essential information, the Karhunen–Loève expansion (KLE) becomes important. The KLE of a random field requires the solution of a large eigenvalue problem. Usually it is solved by a Krylov subspace method with a sparse matrix approximation. We demonstrate the use of sparse hierarchical matrix techniques for this. A log-linear computational cost of the matrix-vector product and a log-linear storage requirement yield an efficient and fast discretisation of the random fields presented.
Editor: Vienna: Springer Vienna
Idioma: Inglês

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Application of hierarchical matrices for computing the Karhunen–Loève expansion

Khoromskij, B. N. ; Litvinenko, A. ; Matthies, H. G.

Vienna: Springer Vienna

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