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Volumn 25, Issue 2, 2003, Pages 749-765

A class of spectral two-level preconditioners

Author keywords

Adaptative preconditioning techniques; Electromagnetic scattering applications; Krylov methods; Low rank correction; Spectral correction; Two level preconditioners

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; MOTIVATION; PARAMETER ESTIMATION; PROBLEM SOLVING; SCATTERING; SPECTRUM ANALYSIS;

EID: 2342520110     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502408591     Document Type: Conference Paper
Times cited : (65)

References (33)
  • 1
    • 0043234061 scopus 로고    scopus 로고
    • Sparse approximate inverse preconditioning for dense linear systems arising in computational electromagnetics
    • G. ALLÉON, M. BENZI, AND L. GIRAUD, Sparse approximate inverse preconditioning for dense linear systems arising in computational electromagnetics, Numer. Algorithms, 16 (1997), pp. 1-15.
    • (1997) Numer. Algorithms , vol.16 , pp. 1-15
    • Alléon, G.1    Benzi, M.2    Giraud, L.3
  • 2
    • 0000734143 scopus 로고    scopus 로고
    • Krylov sequences of maximal length and convergence of GMRES
    • M. ARIOLI, V. PTÁK, AND Z. STRAKOŠ, Krylov sequences of maximal length and convergence of GMRES, BIT, 38 (1998), pp. 636-643.
    • (1998) BIT , vol.38 , pp. 636-643
    • Arioli, M.1    Pták, V.2    Strakoš, Z.3
  • 4
    • 0033470648 scopus 로고    scopus 로고
    • Implicitly restarted and deflated GMRES
    • C. LE CALVEZ AND B. MOLINA, Implicitly restarted and deflated GMRES, Numer. Algorithms, 21 (1999), pp. 261-285.
    • (1999) Numer. Algorithms , vol.21 , pp. 261-285
    • Le Calvez, C.1    Molina, B.2
  • 6
    • 0034359574 scopus 로고    scopus 로고
    • Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism
    • B. CARPENTIERI, I. S. DUFF, AND L. GIRAUD, Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism, Numer. Linear Algebra Appl., 7 (2000), pp. 667-685.
    • (2000) Numer. Linear Algebra Appl. , vol.7 , pp. 667-685
    • Carpentieri, B.1    Duff, I.S.2    Giraud, L.3
  • 7
    • 2342644276 scopus 로고    scopus 로고
    • Combining fast multipole techniques and an approximate inverse preconditioner for large parallel electromagnetics calculations
    • in preparation, CERFACS, Toulouse, France
    • B. CARPENTIERI, I. S. DUFF, L. GIRAUD, AND G. SYLVAND, Combining Fast Multipole Techniques and an Approximate Inverse Preconditioner for Large Parallel Electromagnetics Calculations, Technical report in preparation, CERFACS, Toulouse, France, 2002.
    • (2002) Technical Report
    • Carpentieri, B.1    Duff, I.S.2    Giraud, L.3    Sylvand, G.4
  • 8
    • 0035686426 scopus 로고    scopus 로고
    • Algebraic two-level preconditioners for the Schur complement method
    • L. M. CARVALHO, L. GIRAUD, AND P. LE TALLEC, Algebraic two-level preconditioners for the Schur complement method, SIAM J. Sci. Comput., 22 (2001), pp. 1987-2005.
    • (2001) SIAM J. Sci. Comput. , vol.22 , pp. 1987-2005
    • Carvalho, L.M.1    Giraud, L.2    Le Tallec, P.3
  • 9
    • 2342531207 scopus 로고    scopus 로고
    • Inner-outer methods with deflation for linear systems with multiple right-hand sides
    • Householder Symposium XIII, Pontresina, Switzerland
    • E. DE STURLER, Inner-outer methods with deflation for linear systems with multiple right-hand sides, in Householder Symposium XIII, Proceedings of the Householder Symposium on Numerical Algebra, Pontresina, Switzerland, 1996, pp. 193-196.
    • (1996) Proceedings of the Householder Symposium on Numerical Algebra , pp. 193-196
    • De Sturler, E.1
  • 10
    • 0004109578 scopus 로고
    • Users' guide for the Harwell-Boeing sparse matrix collection
    • CERFACS, Toulouse, France. Also RAL Technical Report RAL 92-086
    • I. S. DUFF, R. G. GRIMES, AND J. G. LEWIS, Users' Guide for the Harwell-Boeing Sparse Matrix Collection, Technical report TR/PA/92/86, CERFACS, Toulouse, France, 1992. Also RAL Technical Report RAL 92-086.
    • (1992) Technical Report , vol.TR-PA-92-86
    • Duff, I.S.1    Grimes, R.G.2    Lewis, J.G.3
  • 11
    • 0030143587 scopus 로고    scopus 로고
    • Restarted GMRES preconditioned by deflation
    • J. ERHEL, K. BURRAGE, AND B. POHL, Restarted GMRES preconditioned by deflation, J. Comput. Appl. Math., 69 (1996), pp. 303-318.
    • (1996) J. Comput. Appl. Math. , vol.69 , pp. 303-318
    • Erhel, J.1    Burrage, K.2    Pohl, B.3
  • 12
    • 0036227210 scopus 로고    scopus 로고
    • On the construction of deflation-based preconditioners
    • J. FRANK AND C. VUIK, On the construction of deflation-based preconditioners, SIAM J. Sci. Comput., 23 (2001), pp. 442-462.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 442-462
    • Frank, J.1    Vuik, C.2
  • 13
    • 0000806356 scopus 로고
    • An implementation of the QMR method based on coupled two-term recurrences
    • R. W. FREUND AND N. M. NACHTIGAL, An implementation of the QMR method based on coupled two-term recurrences., SIAM J. Sci. Comput., 15 (1994), pp. 313-337.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 313-337
    • Freund, R.W.1    Nachtigal, N.M.2
  • 15
    • 0041049302 scopus 로고    scopus 로고
    • Any nonincreasing convergence curve is possible for GMRES
    • A. GREENBAUM, V. PTÁK, AND Z. STRAKOŠ, Any nonincreasing convergence curve is possible for GMRES, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 465-469.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 465-469
    • Greenbaum, A.1    Pták, V.2    Strakoš, Z.3
  • 16
    • 84985401314 scopus 로고
    • Eigenvalue translation based preconditioners for the GMRES(k) method
    • S. A. KHARCHENKO AND A. Yu. YEREMIN, Eigenvalue translation based preconditioners for the GMRES(k) method, Numer. Linear Algebra Appl., 2 (1995), pp. 51-77.
    • (1995) Numer. Linear Algebra Appl. , vol.2 , pp. 51-77
    • Kharchenko, S.A.1    Yeremin, A.Yu.2
  • 17
    • 85160606001 scopus 로고
    • Twofold deflation preconditioning of linear algebraic systems. I. Theory
    • Elegant Mathematics, Inc.
    • L. Yu. KOLOTILINA, Twofold Deflation Preconditioning of Linear Algebraic Systems. I. Theory, Technical report EM-RR 20/95, Elegant Mathematics, Inc., 1995; also available online from http://www.elegant-math.com/abs-emrr.htm.
    • (1995) Technical Report , vol.EM-RR 20-95
    • Kolotilina, L.Yu.1
  • 19
    • 0023982322 scopus 로고
    • On the use of deflation to improve the convergence of conjugate gradient iteration
    • L. MANSFIELD, On the use of deflation to improve the convergence of conjugate gradient iteration, Comm. Appl. Numer. Methods, 4 (1988), pp. 151-156.
    • (1988) Comm. Appl. Numer. Methods , vol.4 , pp. 151-156
    • Mansfield, L.1
  • 20
    • 0000299811 scopus 로고
    • Damped Jacobi preconditioning and coarse grid deflation for conjugate gradient iteration on parallel computers
    • L. MANSFIELD, Damped Jacobi preconditioning and coarse grid deflation for conjugate gradient iteration on parallel computers, SIAM J. Sci. Statist. Comput., 12 (1991), pp. 1314-1323.
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 1314-1323
    • Mansfield, L.1
  • 21
    • 84966225158 scopus 로고
    • An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix
    • J. A. MEIJERINK AND H. A. VAN DER VORST, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comp., 31 (1977), pp. 148-162.
    • (1977) Math. Comp. , vol.31 , pp. 148-162
    • Meijerink, J.A.1    Van Der Vorst, H.A.2
  • 22
    • 0342602167 scopus 로고
    • A restarted GMRES method augmented with eigenvectors
    • R. B. MORGAN, A restarted GMRES method augmented with eigenvectors, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 1154-1171.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 1154-1171
    • Morgan, R.B.1
  • 23
    • 0034144749 scopus 로고    scopus 로고
    • Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations
    • R. B. MORGAN, Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1112-1135.
    • (2000) SIAM J. Matrix Anal. Appl. , vol.21 , pp. 1112-1135
    • Morgan, R.B.1
  • 24
    • 0037249694 scopus 로고    scopus 로고
    • GMRES with deflated restarting
    • R. B. MORGAN, GMRES with deflated restarting, SIAM J. Sci. Comput., 24 (2002), pp. 20-37.
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 20-37
    • Morgan, R.B.1
  • 25
    • 0023331865 scopus 로고
    • Deflation of conjugate gradients with applications to boundary value problems
    • R. A. NICOLAIDES, Deflation of conjugate gradients with applications to boundary value problems, SIAM J. Numer. Anal., 24 (1987), pp. 355-365.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 355-365
    • Nicolaides, R.A.1
  • 26
    • 0023979476 scopus 로고
    • Projection and deflation methods for partial pole assignment in linear state feedback
    • Y. SAAD, Projection and deflation methods for partial pole assignment in linear state feedback, IEEE Trans. Automat. Control, 33 (1988), pp. 290-297.
    • (1988) IEEE Trans. Automat. Control , vol.33 , pp. 290-297
    • Saad, Y.1
  • 27
    • 0031534369 scopus 로고    scopus 로고
    • Analysis of augmented Krylov subspace methods
    • Y. SAAD, Analysis of augmented Krylov subspace methods, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 435-449.
    • (1997) SIAM J. Matrix Anal. Appl. , vol.18 , pp. 435-449
    • Saad, Y.1
  • 28
    • 84985408358 scopus 로고
    • ILUT: A dual threshold incomplete LU factorization
    • Y. SAAD, ILUT: A dual threshold incomplete LU factorization, Numer. Linear Algebra Appl., 1 (1994), pp. 387-402.
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 387-402
    • Saad, Y.1
  • 29
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 30
    • 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
  • 32
    • 0000005482 scopus 로고
    • Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems
    • H. A. VAN DER VORST, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 631-644.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 631-644
    • Van Der Vorst, H.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.