Application of hierarchical matrices for computing the Karhunen-Loève expansion
type: Item
instance of: scholarly article
title: Application of hierarchical matrices for computing the Karhunen-Loève expansion
zbMATH Open document ID: 1162.65306
author: Boris N. Khoromskij
author: Alexander Litvinenko
author: Hermann G. Matthies
published in: Computing
publication date: 2009-04-27T00:00:00Z
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 45C05
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 5547551
zbMATH Keywords: numerical examples
zbMATH Keywords: uncertainty quantification
zbMATH Keywords: finite element
zbMATH Keywords: random fields
zbMATH Keywords: Karhunen-Loève expansion
zbMATH Keywords: large eigenvalue problem
zbMATH Keywords: Krylov subspace method
zbMATH Keywords: sparse matrix approximation
zbMATH Keywords: sparse hierarchical matrix
Wikidata QID: Q57524801
describes a project that uses: JDQR
describes a project that uses: TRLan
describes a project that uses: ARPACK
describes a project that uses: hlib
describes a project that uses: FFTW
describes a project that uses: JDQZ
MaRDI profile type: Publication
full work available at URL: s00607-008-0018-3
OpenAlex ID: W2128811293
cites work: The Numerical Solution of Integral Equations of the Second Kind
cites work: Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
cites work: A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
cites work: Templates for the Solution of Algebraic Eigenvalue Problems
cites work: Approximation of boundary element matrices
cites work: Stabilized rounded addition of hierarchical matrices
cites work: Adaptive low-rank approximation of collocation matrices
cites work: Hybrid cross approximation of integral operators
cites work: Construction and complexity of hierarchical matrices
cites work: Computational aspects of the stochastic finite element method
cites work: Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering
cites work: Q3997987
cites work: A theory of pseudoskeleton approximations
cites work: Construction and arithmetics of \(\mathcal H\)-matrices
cites work: A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems
cites work: A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
cites work: Hierarchical matrices based on a weak admissibility criterion
cites work: Hierarchical Kronecker tensor-product approximations
cites work: Q4202615
cites work: Q5477981
cites work: ARPACK Users' Guide
cites work: Q4131338
cites work: Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
cites work: Iterative solution of systems of linear equations arising in the context of stochastic finite elements
cites work: Q5287558
cites work: Numerical methods for large eigenvalue problems
cites work: Sparse finite elements for elliptic problems with stochastic loading
cites work: Sparse finite elements for stochastic elliptic problems --- higher order moments
cites work: Karhunen-Loève approximation of random fields by generalized fast multipole methods
cites work: Fourier mode analysis of multigrid methods for partial differential equations with random coefficients
cites work: Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients
cites work: The Homogeneous Chaos
cites work: Thick-restart Lanczos method for large symmetric eigenvalue problems
DOI: 10.1007/S00607-008-0018-3
description: scientific article; zbMATH DE number 5547551