메뉴 건너뛰기




Volumn 84, Issue 1-2, 2009, Pages 49-67

Application of hierarchical matrices for computing the Karhunen- loève expansion

Author keywords

Data sparse approximation; Eigenvalue computation; Hierarchical matrix; Karhunen Lo ve expansion; Random fields; Uncertainty quantification

Indexed keywords

DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL OPERATORS; MODELS; NEMATIC LIQUID CRYSTALS; RANDOM PROCESSES; STOCHASTIC MODELS;

EID: 63449128673     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-008-0018-3     Document Type: Article
Times cited : (79)

References (42)
  • 1
    • 0012707577 scopus 로고    scopus 로고
    • The numerical solution of integral equations of the second kind
    • Cambridge University Press, Cambridge
    • Atkinson KE (1997) The numerical solution of integral equations of the second kind. Cambridge monographs on applied and computational mathematics, vol 4. Cambridge University Press, Cambridge
    • (1997) Cambridge Monographs on Applied and Computational Mathematics , vol.4
    • Atkinson, K.E.1
  • 2
    • 13844319204 scopus 로고    scopus 로고
    • Galerkin finite element approximations of stochastic elliptic partial differential equations
    • electronic
    • Babuška I, Tempone R, Zouraris GE (2004) Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J Numer Anal 42(2):800-825 (electronic)
    • (2004) SIAM J Numer Anal , vol.42 , Issue.2 , pp. 800-825
    • Babuška, I.1    Tempone, R.2    Zouraris, G.E.3
  • 3
    • 34548216854 scopus 로고    scopus 로고
    • A stochastic collocation method for elliptic partial differential equations with random input data
    • electronic
    • Babuška I, Nobile F, Tempone R (2007) A stochastic collocation method for elliptic partial differential equations with random input data. SIAM J Numer Anal 45(3):1005-1034 (electronic)
    • (2007) SIAM J Numer Anal , vol.45 , Issue.3 , pp. 1005-1034
    • Babuška, I.1    Nobile, F.2    Tempone, R.3
  • 4
    • 0003893794 scopus 로고    scopus 로고
    • Templates for the solution of algebraic eigenvalue problems- practical guide
    • Bai Z, Demmel J, Dongarra J, Ruhe A, van der Vorst H (eds) Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • Bai Z, Demmel J, Dongarra J, Ruhe A, van der Vorst H (eds) (2000) Templates for the solution of algebraic eigenvalue problems- practical guide, vol 11 of Software, Environments, and Tools. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • (2000) Software, Environments, and Tools , vol.11
  • 5
    • 5844381624 scopus 로고    scopus 로고
    • Approximation of boundary element matrices
    • M Bebendorf 2000 Approximation of boundary element matrices Numer Math 86 4 565 589
    • (2000) Numer Math , vol.86 , Issue.4 , pp. 565-589
    • Bebendorf, M.1
  • 6
    • 34248574744 scopus 로고    scopus 로고
    • Stabilized rounded addition of hierarchical matrices
    • M Bebendorf W Hackbusch 2007 Stabilized rounded addition of hierarchical matrices Numer Linear Algebra Appl 14 5 407 423
    • (2007) Numer Linear Algebra Appl , vol.14 , Issue.5 , pp. 407-423
    • Bebendorf, M.1    Hackbusch, W.2
  • 7
    • 0041841599 scopus 로고    scopus 로고
    • Adaptive low-rank approximation of collocation matrices
    • M Bebendorf S Rjasanow 2003 Adaptive low-rank approximation of collocation matrices Computing 70 1 1 24
    • (2003) Computing , vol.70 , Issue.1 , pp. 1-24
    • Bebendorf, M.1    Rjasanow, S.2
  • 8
    • 24044501239 scopus 로고    scopus 로고
    • Hybrid cross approximation of integral operators
    • S Börm L Grasedyck 2005 Hybrid cross approximation of integral operators Numer Math 101 2 221 249
    • (2005) Numer Math , vol.101 , Issue.2 , pp. 221-249
    • Börm, S.1    Grasedyck, L.2
  • 10
    • 33847247390 scopus 로고    scopus 로고
    • Computational aspects of the stochastic finite element method
    • M Eiermann OG Ernst E Ullmann 2007 Computational aspects of the stochastic finite element method Comput Vis Sci 10 1 3 15
    • (2007) Comput Vis Sci , vol.10 , Issue.1 , pp. 3-15
    • Eiermann, M.1    Ernst, O.G.2    Ullmann, E.3
  • 11
    • 12344334601 scopus 로고    scopus 로고
    • Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering
    • HC Elman OG Ernst DP O'Leary M Stewart 2005 Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering Comput Methods Appl Mech Eng 194 9-11 1037 1055
    • (2005) Comput Methods Appl Mech Eng , vol.194 , Issue.9-11 , pp. 1037-1055
    • Elman, H.C.1    Ernst, O.G.2    O'Leary, D.P.3    Stewart, M.4
  • 12
    • 0031636309 scopus 로고    scopus 로고
    • FFTW: An adaptive software architecture for the FFT
    • IEEE, Seattle, WA
    • Frigo M, Johnson S (1998) FFTW: An adaptive software architecture for the FFT. In: Proc. ICASSP, IEEE, Seattle, WA, (3):1381-1384. http://www.fftw.org
    • (1998) Proc. ICASSP , Issue.3 , pp. 1381-1384
    • Frigo, M.1    Johnson, S.2
  • 13
    • 0026238497 scopus 로고
    • Spectral stochastic finite-element formulation for reliability analysis
    • R Ghanem D Spanos 1991 Spectral stochastic finite-element formulation for reliability analysis J Eng Mech 117 10 2351 2370
    • (1991) J Eng Mech , vol.117 , Issue.10 , pp. 2351-2370
    • Ghanem, R.1    Spanos, D.2
  • 16
  • 17
    • 0141829814 scopus 로고    scopus 로고
    • Construction arithmetics of H-matrices
    • L Grasedyck W Hackbusch 2003 Construction arithmetics of H-matrices Computing 70 4 295 334
    • (2003) Computing , vol.70 , Issue.4 , pp. 295-334
    • Grasedyck, L.1    Hackbusch, W.2
  • 18
    • 0002133258 scopus 로고    scopus 로고
    • A sparse H-matrix arithmetic. II. Application to multi-dimensional problems
    • W Hackbusch BN Khoromskij 2000 A sparse H-matrix arithmetic. II. Application to multi-dimensional problems Computing 64 1 21 47
    • (2000) Computing , vol.64 , Issue.1 , pp. 21-47
    • Hackbusch, W.1    Khoromskij, B.N.2
  • 19
    • 0003707754 scopus 로고
    • Integral equations
    • Birkhäuser Verlag, Basel, 1995. Theory and numerical treatment, Translated and revised by the author from the 1989 German original
    • Hackbusch W (1995) Integral equations, vol 120 of International Series of Numerical Mathematics. Birkhäuser Verlag, Basel, 1995. Theory and numerical treatment, Translated and revised by the author from the 1989 German original
    • (1995) International Series of Numerical Mathematics , vol.120
    • Hackbusch, W.1
  • 20
    • 0032637646 scopus 로고    scopus 로고
    • A sparse matrix arithmetic based on H-matrices. I. Introduction to H-matrices
    • W Hackbusch 1999 A sparse matrix arithmetic based on H-matrices. I. Introduction to H-matrices Computing 62 2 89 108
    • (1999) Computing , vol.62 , Issue.2 , pp. 89-108
    • Hackbusch, W.1
  • 22
    • 10644283019 scopus 로고    scopus 로고
    • Hierarchical matrices based on a weak admissibility criterion
    • W Hackbusch BN Khoromskij R Kriemann 2004 Hierarchical matrices based on a weak admissibility criterion Computing 73 3 207 243
    • (2004) Computing , vol.73 , Issue.3 , pp. 207-243
    • Hackbusch, W.1    Khoromskij, B.N.2    Kriemann, R.3
  • 24
    • 0242522234 scopus 로고
    • White noise-an infinite-dimensional calculus
    • Kluwer Academic Publishers Group, Dordrecht
    • Hida T, Kuo H-H, Potthoff J, Streit L (1993) White noise-an infinite-dimensional calculus, vol 253 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht (1993)
    • (1993) Mathematics and Its Applications , vol.253
    • Hida, T.1    Kuo, H.-H.2    Potthoff, J.3    Streit, L.4
  • 25
    • 13844321715 scopus 로고    scopus 로고
    • Numerical solution of systems with stochastic uncertainties
    • Ph.D. Thesis, TU Braunschweig, Germany
    • Keese A (2004) Numerical solution of systems with stochastic uncertainties. A general purpose framework for stochastic finite elements. Ph.D. Thesis, TU Braunschweig, Germany
    • (2004) A General Purpose Framework for Stochastic Finite Elements
    • Keese, A.1
  • 26
    • 0000094594 scopus 로고
    • An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
    • C Lanczos 1995 An iteration method for the solution of the eigenvalue problem of linear differential and integral operators J Res Nat Bur Standards 45 255 282
    • (1995) J Res Nat Bur Standards , vol.45 , pp. 255-282
    • Lanczos, C.1
  • 27
    • 0038436804 scopus 로고    scopus 로고
    • ARPACK users' guide. Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods
    • Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • Lehoucq RB, Sorensen DC, Yang C (1998) ARPACK users' guide. Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods, vol 6 of Software, Environments, and Tools. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • (1998) Software, Environments, and Tools , vol.6
    • Lehoucq, R.B.1    Sorensen, D.C.2    Yang, C.3
  • 28
    • 4244033811 scopus 로고
    • Probability theory I
    • 4th edn. Springer, New York
    • Loève, M (1977) Probability theory I. Graduate Texts in Mathematics, vol 45, 6, 4th edn. Springer, New York
    • (1977) Graduate Texts in Mathematics , vol.6-45
    • Loève, M.1
  • 30
    • 13844308726 scopus 로고    scopus 로고
    • Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
    • HG Matthies A Keese 2005 Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations Comput Methods Appl Mech Eng 194 12-16 1295 1331
    • (2005) Comput Methods Appl Mech Eng , vol.194 , Issue.12-16 , pp. 1295-1331
    • Matthies, H.G.1    Keese, A.2
  • 31
    • 0342844513 scopus 로고    scopus 로고
    • Iterative solution of systems of linear equations arising in the context of stochastic finite elements
    • MF Pellissetti R Ghanem 2000 Iterative solution of systems of linear equations arising in the context of stochastic finite elements Adv Eng Softw 31 8-9 607 616
    • (2000) Adv Eng Softw , vol.31 , Issue.8-9 , pp. 607-616
    • Pellissetti, M.F.1    Ghanem, R.2
  • 33
    • 0345100081 scopus 로고
    • Functional analysis
    • Dover Publications Inc., New York, 1990. Translated from the second French edition by Leo F. Boron, Reprint of the 1955 original
    • Riesz F, Sz.-Nagy B (1990) Functional analysis. Dover Books on Advanced Mathematics. Dover Publications Inc., New York, 1990. Translated from the second French edition by Leo F. Boron, Reprint of the 1955 original
    • (1990) Dover Books on Advanced Mathematics
    • Riesz, F.1    Sz.-Nagy, B.2
  • 35
    • 0242370956 scopus 로고    scopus 로고
    • Sparse finite elements for elliptic problems with stochastic loading
    • C Schwab RA Todor 2003 Sparse finite elements for elliptic problems with stochastic loading Numer Math 95 4 707 734
    • (2003) Numer Math , vol.95 , Issue.4 , pp. 707-734
    • Schwab, C.1    Todor, R.A.2
  • 36
    • 0141957096 scopus 로고    scopus 로고
    • Sparse finite elements for stochastic elliptic problems-higher order moments
    • C Schwab RA Todor 2003 Sparse finite elements for stochastic elliptic problems-higher order moments Computing 71 43 63
    • (2003) Computing , vol.71 , pp. 43-63
    • Schwab, C.1    Todor, R.A.2
  • 37
    • 33746346426 scopus 로고    scopus 로고
    • Karhunen-Loève approximation of random fields by generalized fast multipole methods
    • C Schwab RA Todor 2006 Karhunen-Loève approximation of random fields by generalized fast multipole methods J Comput Phys 217 1 100 122
    • (2006) J Comput Phys , vol.217 , Issue.1 , pp. 100-122
    • Schwab, C.1    Todor, R.A.2
  • 38
    • 34248150929 scopus 로고    scopus 로고
    • Fourier mode analysis of multigrid methods for partial differential equations with random coefficients
    • B Seynaeve E Rosseel B Nicolaï S Vandewalle 2007 Fourier mode analysis of multigrid methods for partial differential equations with random coefficients J Comput Phys 224 1 132 149
    • (2007) J Comput Phys , vol.224 , Issue.1 , pp. 132-149
    • Seynaeve, B.1    Rosseel, E.2    Nicolaï, B.3    Vandewalle, S.4
  • 39
    • 34047123580 scopus 로고    scopus 로고
    • Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients
    • RA Todor C Schwab 2007 Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients IMA J Numer Anal 27 2 232 261
    • (2007) IMA J Numer Anal , vol.27 , Issue.2 , pp. 232-261
    • Todor, R.A.1    Schwab, C.2
  • 41
    • 0000786435 scopus 로고
    • The homogeneous chaos
    • N Wiener 1938 The homogeneous chaos Am J Math 60 897 936
    • (1938) Am J Math , vol.60 , pp. 897-936
    • Wiener, N.1
  • 42
    • 0006377434 scopus 로고    scopus 로고
    • Thick-restart Lanczos method for large symmetric eigenvalue problems
    • electronic
    • Wu K, Simon H (2000) Thick-restart Lanczos method for large symmetric eigenvalue problems. SIAM J Matrix Anal Appl 22(2):602-616 (electronic)
    • (2000) SIAM J Matrix Anal Appl , vol.22 , Issue.2 , pp. 602-616
    • Wu, K.1    Simon, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.