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Volumn 65, Issue 8, 2006, Pages 1186-1196

Algebraic multigrid methods for solving generalized eigenvalue problems

Author keywords

Algebraic multigrid methods; Generalized eigenvalue problems

Indexed keywords

BOUNDARY VALUE PROBLEMS; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; INVERSE PROBLEMS; ITERATIVE METHODS; MATRIX ALGEBRA;

EID: 32444445032     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1478     Document Type: Article
Times cited : (20)

References (22)
  • 2
    • 0001237755 scopus 로고
    • Analysis of a multilevel inverse iteration procedure for eigenvalue problems
    • Bank R. Analysis of a multilevel inverse iteration procedure for eigenvalue problems. SIAM Journal on Numerical Analysis 1982; 19:886-898.
    • (1982) SIAM Journal on Numerical Analysis , vol.19 , pp. 886-898
    • Bank, R.1
  • 4
    • 0000323375 scopus 로고    scopus 로고
    • Multigrid methods for nearly singular linear equations and eigenvalue problems
    • Cai Z, Mandel J, McCormick S. Multigrid methods for nearly singular linear equations and eigenvalue problems. SIAM Journal on Numerical Analysis 1997; 34:178-200.
    • (1997) SIAM Journal on Numerical Analysis , vol.34 , pp. 178-200
    • Cai, Z.1    Mandel, J.2    McCormick, S.3
  • 5
    • 20644466062 scopus 로고
    • Adaptive multigrid techniques for large scale eigenvalue problems: Solutions of the Schrödinger problem in two and three dimensions
    • Costiner S, Ta'asan S. Adaptive multigrid techniques for large scale eigenvalue problems: solutions of the Schrödinger problem in two and three dimensions, Physical Review E 1995; 51:3704-3717.
    • (1995) Physical Review E , vol.51 , pp. 3704-3717
    • Costiner, S.1    Ta'asan, S.2
  • 8
    • 0001171887 scopus 로고
    • On the computation of approximate eigenvalues and eigenfunctions by means of a multigrid method
    • Hackbusch W. On the computation of approximate eigenvalues and eigenfunctions by means of a multigrid method. SIAM Journal on Numerical Analysis 1979; 16:201-215.
    • (1979) SIAM Journal on Numerical Analysis , vol.16 , pp. 201-215
    • Hackbusch, W.1
  • 9
    • 0034462939 scopus 로고    scopus 로고
    • On multigrid methods for the eigenvalue computation of nonselfadjoint elliptic operators
    • Heuveline V, Bertsch C. On multigrid methods for the eigenvalue computation of nonselfadjoint elliptic operators. East-West Journal of Numerical Mathematics 2000; 8:275-297.
    • (2000) East-West Journal of Numerical Mathematics , vol.8 , pp. 275-297
    • Heuveline, V.1    Bertsch, C.2
  • 11
    • 1842564087 scopus 로고    scopus 로고
    • An algebraic multigrid method for a class of elliptic differential systems
    • Borzì A, Borzì G. An algebraic multigrid method for a class of elliptic differential systems. SIAM Journal on Scientific Computing 2003; 25(1):302-323.
    • (2003) SIAM Journal on Scientific Computing , vol.25 , Issue.1 , pp. 302-323
    • Borzì, A.1    Borzì, G.2
  • 12
    • 0040354541 scopus 로고    scopus 로고
    • Algebraic multigrid (AMG): An introduction with applications
    • March
    • Stüben K. Algebraic multigrid (AMG): an introduction with applications. GMD Report 53, March 1999.
    • (1999) GMD Report 53
    • Stüben, K.1
  • 13
    • 84966233568 scopus 로고
    • Multi-level adaptive solutions to boundary-value problems
    • Brandt A. Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation 1977; 31:333-390.
    • (1977) Mathematics of Computation , vol.31 , pp. 333-390
    • Brandt, A.1
  • 14
    • 0035586115 scopus 로고    scopus 로고
    • A geometric theory for preconditioned inverse iteration, I: Extrema of the Rayleigh quotient
    • Neymeyr K. A geometric theory for preconditioned inverse iteration, I: extrema of the Rayleigh quotient. Linear Algebra and its Applications 2001; 322:61-85.
    • (2001) Linear Algebra and Its Applications , vol.322 , pp. 61-85
    • Neymeyr, K.1
  • 15
    • 0035585865 scopus 로고    scopus 로고
    • A geometric theory for preconditioned inverse iteration, II: Convergence estimates
    • Neymeyr K. A geometric theory for preconditioned inverse iteration, II: convergence estimates. Linear Algebra and its Applications 2001; 322:87-104.
    • (2001) Linear Algebra and Its Applications , vol.322 , pp. 87-104
    • Neymeyr, K.1
  • 16
    • 32044463478 scopus 로고    scopus 로고
    • A geometric theory for preconditioned inverse iteration, III: A short and sharp convergence estimate for generalized eigenvalue problems
    • Knyazev AV, Neymeyr K. A geometric theory for preconditioned inverse iteration, III: a short and sharp convergence estimate for generalized eigenvalue problems. Linear Algebra and its Applications 2003; 358: 95-114.
    • (2003) Linear Algebra and Its Applications , vol.358 , pp. 95-114
    • Knyazev, A.V.1    Neymeyr, K.2
  • 17
    • 0036223489 scopus 로고    scopus 로고
    • Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method
    • Knyazev AV. Toward the optimal preconditioned eigensolver: locally optimal block preconditioned conjugate gradient method. SIAM Journal on Scientific Computing 2001; 23:517-541.
    • (2001) SIAM Journal on Scientific Computing , vol.23 , pp. 517-541
    • Knyazev, A.V.1
  • 18
    • 32444450330 scopus 로고    scopus 로고
    • Algebraic multigrid methods for solving eigenvalue problems
    • Borzì G, Borzì A. Algebraic multigrid methods for solving eigenvalue problems. EMG 2002, Hohenwart Forum, 2002.
    • (2002) EMG 2002, Hohenwart Forum
    • Borzì, G.1    Borzì, A.2
  • 19
    • 51249191449 scopus 로고
    • Evaluation of eigensolution of discrete space diffusion equation
    • Buffoni G. Evaluation of eigensolution of discrete space diffusion equation. Calcolo 1967; 42:169-177.
    • (1967) Calcolo , vol.42 , pp. 169-177
    • Buffoni, G.1
  • 20
    • 84966222272 scopus 로고
    • SOR-methods for the eigenvalue problem with large sparse matrices
    • Ruhe A. SOR-methods for the eigenvalue problem with large sparse matrices. Mathematics of Computation 1974; 28:695-710.
    • (1974) Mathematics of Computation , vol.28 , pp. 695-710
    • Ruhe, A.1
  • 22
    • 0031100472 scopus 로고    scopus 로고
    • Eigenmodes of isospectral drums
    • Driscoll TA. Eigenmodes of isospectral drums. SIAM Review 1997; 39:1-17.
    • (1997) SIAM Review , vol.39 , pp. 1-17
    • Driscoll, T.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.