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Volumn 19, Issue 4, 1998, Pages 1045-1073

A truncated RQ iteration for large scale eigenvalue calculations

Author keywords

Arnoldi method; Deflation; Eigenvalues; Krylov methods; Lanczos method; Preconditioning; Restarting

Indexed keywords


EID: 0032348061     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479896305398     Document Type: Article
Times cited : (25)

References (23)
  • 1
    • 1542498748 scopus 로고    scopus 로고
    • Iterative methods for the computation of a few eigenvalues of a large symmetric matrix
    • J. BAGLAMA, D. CALVETTI, AND L. REICHEL, Iterative methods for the computation of a few eigenvalues of a large symmetric matrix. BIT, 36 (1996), pp. 400-421.
    • (1996) BIT , vol.36 , pp. 400-421
    • Baglama, J.1    Calvetti, D.2    Reichel, L.3
  • 3
    • 85033886464 scopus 로고    scopus 로고
    • SRRIT-A FORTRAN subroutine to calculate the dominant invariant subspace of a nonsymmetric matrix
    • to appear
    • Z. BAI AND G. W. STEWART, SRRIT-A FORTRAN subroutine to calculate the dominant invariant subspace of a nonsymmetric matrix, ACM Trans. Math. Software, to appear.
    • ACM Trans. Math. Software
    • Bai, Z.1    Stewart, G.W.2
  • 4
    • 0040064702 scopus 로고
    • The Arnoldi-Tchebycheff algorithm for solving large nonsymmetric eigenproblems
    • CERFACS, Toulouse, France
    • T. BRACONNIER, The Arnoldi-Tchebycheff Algorithm for Solving Large Nonsymmetric Eigenproblems, Technical Report TR/PA/93/25. CERFACS, Toulouse, France, 1993.
    • (1993) Technical Report TR/PA/93/25
    • Braconnier, T.1
  • 5
    • 0002654780 scopus 로고
    • An implicitly restarted Lanczos method for large symmetric eigenvalue problems
    • D. CALVETTI, L. REICHEL, AND D. C. SORENSEN, An implicitly restarted Lanczos method for large symmetric eigenvalue problems, ETNA, 2 (1994), pp. 1-21.
    • (1994) ETNA , vol.2 , pp. 1-21
    • Calvetti, D.1    Reichel, L.2    Sorensen, D.C.3
  • 7
    • 84966217951 scopus 로고
    • Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization
    • J. DANIEL, W. B. GRAGG, L. KAUFMAN, AND G. W. STEWART, Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization, Math. Comp., 30 (1976), pp. 772-795.
    • (1976) Math. Comp. , vol.30 , pp. 772-795
    • Daniel, J.1    Gragg, W.B.2    Kaufman, L.3    Stewart, G.W.4
  • 8
    • 0027610227 scopus 로고
    • Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration
    • I. S. DUFF AND J. A. SCOTT, Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration, ACM Trans. Math. Software, 19 (1993), pp. 137-159.
    • (1993) ACM Trans. Math. Software , vol.19 , pp. 137-159
    • Duff, I.S.1    Scott, J.A.2
  • 9
    • 0032131701 scopus 로고    scopus 로고
    • Jacobi-Davidson style QR and QZ algorithm for partial reduction of matrix pencils
    • to appear
    • D. R. FOKKEMA, G. L. G. SLEIJPEN, AND H. A. VAN DER VORST, Jacobi-Davidson style QR and QZ algorithm for partial reduction of matrix pencils, SIAM J. Sci. Comput., to appear.
    • SIAM J. Sci. Comput.
    • Fokkema, D.R.1    Sleijpen, G.L.G.2    Van Der Vorst, H.A.3
  • 11
    • 0030502142 scopus 로고    scopus 로고
    • Deflation techniques for an implicitly restarted Arnoldi iteration
    • R. B. LEHOUCQ AND D. C. SORENSEN, Deflation techniques for an implicitly restarted Arnoldi iteration, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 789-821.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 789-821
    • Lehoucq, R.B.1    Sorensen, D.C.2
  • 13
    • 0030353046 scopus 로고    scopus 로고
    • On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
    • R. B. MORGAN, On restarting the Arnoldi method for large nonsymmetric eigenvalue problems, Math. Comp., 65 (1996), pp. 1213-1230.
    • (1996) Math. Comp. , vol.65 , pp. 1213-1230
    • Morgan, R.B.1
  • 14
    • 0001409002 scopus 로고
    • The rational Krylov algorithm for nonsymmetric eigenvalue, problems, III: Complex shifts for real matrices
    • A. RUHE, The rational Krylov algorithm for nonsymmetric eigenvalue, problems, III: Complex shifts for real matrices, BIT, 34 (1994), pp. 165-176.
    • (1994) BIT , vol.34 , pp. 165-176
    • Ruhe, A.1
  • 15
    • 43949153380 scopus 로고
    • Rational Krylov algorithms for nonsymmetric eigenvalue, problems, II: Matrix pairs
    • A. RUHE, Rational Krylov algorithms for nonsymmetric eigenvalue, problems, II: Matrix pairs, Linear Algebra Appl., 197/198 (1994), pp. 283-295.
    • (1994) Linear Algebra Appl. , vol.197-198 , pp. 283-295
    • Ruhe, A.1
  • 16
    • 0004001591 scopus 로고
    • Rational Krylov, a practical algorithm for large sparse nonsymmetric matrix pencils
    • Computer Science Division (EECS), University of California, Berkeley, CA
    • A. RUHE, Rational Krylov, a Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils, Technical Report UCB/CSD-95-871 (revised), Computer Science Division (EECS), University of California, Berkeley, CA, 1995.
    • (1995) Technical Report UCB/CSD-95-871 (Revised)
    • Ruhe, A.1
  • 18
    • 0001654663 scopus 로고
    • An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices
    • J. A. SCOTT, An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices, ACM Trans. Math. Soft., 21 (1995), pp. 432-475.
    • (1995) ACM Trans. Math. Soft. , vol.21 , pp. 432-475
    • Scott, J.A.1
  • 19
    • 0030560293 scopus 로고    scopus 로고
    • A Jacobi-Davidson iteration method for linear eigenvalue problems
    • G. L. G. SLEIJPEN AND H. A. VAN DER VORST, A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 401-425.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 401-425
    • Sleijpen, G.L.G.1    Van Der Vorst, H.A.2
  • 20
    • 1542498668 scopus 로고    scopus 로고
    • Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems
    • G. L. G. SLEIJPEN, J. G. L. BOOTEN, D. R. FOKKEMA, AND H. A. VAN DER VORST, Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems, BIT, 6 (1996), pp. 595-633.
    • (1996) BIT , vol.6 , pp. 595-633
    • Sleijpen, G.L.G.1    Booten, J.G.L.2    Fokkema, D.R.3    Van Der Vorst, H.A.4
  • 21
    • 0000322706 scopus 로고
    • Implicit application of polynomial filters in a k-step Arnoldi method
    • D. C. SORENSEN, Implicit application of polynomial filters in a k-step Arnoldi method, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 357-385.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 357-385
    • Sorensen, D.C.1
  • 22
    • 85033884007 scopus 로고    scopus 로고
    • A truncated RQ-iteration for large scale eigenvalue calculations
    • Department of Computational and Applied Mathematics, Rice Univeristy, Houston, TX
    • D. C. SORENSEN AND C. YANG, A Truncated RQ-Iteration for Large Scale Eigenvalue Calculations, Technical Report TR96-06, Department of Computational and Applied Mathematics, Rice Univeristy, Houston, TX, 1996.
    • (1996) Technical Report TR96-06
    • Sorensen, D.C.1    Yang, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.