메뉴 건너뛰기




Volumn 26, Issue 4, 2005, Pages 1001-1021

Breakdown-free gmres for singular systems

Author keywords

Iterative method; Krylov subspace; Linear system; Singular matrix

Indexed keywords

KRYLOV SUBSPACE; SINGULAR MATRIX;

EID: 27144454401     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/S0895479803437803     Document Type: Article
Times cited : (77)

References (19)
  • 1
    • 0002205748 scopus 로고
    • Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations
    • O. AXELSSON, Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations, Linear Algebra Appl., 29 (1980), pp. 1-16.
    • (1980) Linear Algebra Appl. , vol.29 , pp. 1-16
    • Axelsson, O.1
  • 2
    • 0003270351 scopus 로고
    • Nonnegative matrices in the mathematical sciences
    • SIAM, Philadelphia
    • A. BERMAN AND R. J. PLEMMONS, Nonnegative Matrices in the Mathematical Sciences, Classics Appl. Math. 9, SIAM, Philadelphia, 1994.
    • (1994) Classics Appl. Math. , vol.9
    • Berman, A.1    Plemmons, R.J.2
  • 5
    • 0034399370 scopus 로고    scopus 로고
    • GMRES-type methods for inconsistent systems
    • D. CALVETTI, B. LEWIS, AND L. REICHEL, GMRES-type methods for inconsistent systems, Linear Algebra Appl., 316 (2000), pp. 157-169.
    • (2000) Linear Algebra Appl. , vol.316 , pp. 157-169
    • Calvetti, D.1    Lewis, B.2    Reichel, L.3
  • 6
    • 0013183906 scopus 로고    scopus 로고
    • On the choice of subspace for iterative methods for linear discrete ill-posed problems
    • D. CALVETTI, B. LEWIS, AND L. REICHEL, On the choice of subspace for iterative methods for linear discrete ill-posed problems, Int. J. Appl. Math. Comput. Sci., 11 (2001), pp. 1069-1092.
    • (2001) Int. J. Appl. Math. Comput. Sci. , vol.11 , pp. 1069-1092
    • Calvetti, D.1    Lewis, B.2    Reichel, L.3
  • 7
    • 0042232525 scopus 로고    scopus 로고
    • GMRES, L-curves, and discrete ill-posed problems
    • D. CALVETTI, B. LEWIS, AND L. REICHEL, GMRES, L-curves, and discrete ill-posed problems, BIT, 42 (2002), pp. 44-65.
    • (2002) BIT , vol.42 , pp. 44-65
    • Calvetti, D.1    Lewis, B.2    Reichel, L.3
  • 8
    • 31244433876 scopus 로고    scopus 로고
    • A note on Krylov subspace methods for singular systems
    • Z.-H. CAO AND M. WANG, A note on Krylov subspace methods for singular systems, Linear Algebra Appl., 350 (2002), pp. 285-288.
    • (2002) Linear Algebra Appl. , vol.350 , pp. 285-288
    • Cao, Z.-H.1    Wang, M.2
  • 10
    • 0001538079 scopus 로고
    • On the solution of singular linear systems of algebraic equations by semiiterative methods
    • M. EIERMANN, I. MAREK, AND W. NIETHAMMER, On the solution of singular linear systems of algebraic equations by semiiterative methods, Numer. Math., 53 (1988), pp. 265-283.
    • (1988) Numer. Math. , vol.53 , pp. 265-283
    • Eiermann, M.1    Marek, I.2    Niethammer, W.3
  • 11
    • 0040957230 scopus 로고
    • On the application of orthogonal polynomials to the iterative solution of singular systems of equations
    • J. Dongarra, I. Duff, P. Gaffney, and S. McKee, eds., Ellis Horwood, Chichester, UK
    • M. EIERMANN AND L. REICHEL, On the application of orthogonal polynomials to the iterative solution of singular systems of equations, in Vector and Parallel Computing Issues in Applied Research and Development, J. Dongarra, I. Duff, P. Gaffney, and S. McKee, eds., Ellis Horwood, Chichester, UK, 1989, pp. 285-297.
    • (1989) Vector and Parallel Computing Issues in Applied Research and Development , pp. 285-297
    • Eiermann, M.1    Reichel, L.2
  • 12
    • 84985316667 scopus 로고
    • On the use of two QMR algorithms for solving singular systems and application in Markov chain modeling
    • R. FREUND AND M. HOCHBRUCK, On the use of two QMR algorithms for solving singular systems and application in Markov chain modeling, Numer. Linear Algebra Appl., 1 (1994), pp. 403-420.
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 403-420
    • Freund, R.1    Hochbruck, M.2
  • 13
    • 13344267706 scopus 로고
    • Regularization Tools: A MATLAB package for analysis and solution of discrete ill-posed problems
    • P.C. HANSEN, Regularization Tools: A MATLAB package for analysis and solution of discrete ill-posed problems, Numer. Algorithms, 6 (1994), pp. 1-35.
    • (1994) Numer. Algorithms , vol.6 , pp. 1-35
    • Hansen, P.C.1
  • 14
    • 0032280255 scopus 로고    scopus 로고
    • The idea behind Krylov methods
    • I. C. F. IPSEN AND C. D. MEYER, The idea behind Krylov methods, Amer. Math. Monthly, 105 (1998), pp. 889-899.
    • (1998) Amer. Math. Monthly , vol.105 , pp. 889-899
    • Ipsen, I.C.F.1    Meyer, C.D.2
  • 15
    • 0004967825 scopus 로고
    • Block cyclic SOR for Markov chains with p-cyclic infinitesimal generator
    • K. KONTOVALIS, R. J. PLEMMONS, AND W. J. STEWART, Block cyclic SOR for Markov chains with p-cyclic infinitesimal generator, Linear Algebra Appl., 154/156 (1991), pp. 145-223.
    • (1991) Linear Algebra Appl. , vol.154-156 , pp. 145-223
    • Kontovalis, K.1    Plemmons, R.J.2    Stewart, W.J.3
  • 17
    • 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
  • 18
    • 0035885349 scopus 로고    scopus 로고
    • DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems
    • A. SIDI, DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems, Linear Algebra Appl., 335 (2001), pp. 189-204.
    • (2001) Linear Algebra Appl. , vol.335 , pp. 189-204
    • Sidi, A.1
  • 19
    • 84968469566 scopus 로고
    • A breakdown-free variation of the nonsymmetric Lanczos algorithm
    • Q. YE, A breakdown-free variation of the nonsymmetric Lanczos algorithm, Math. Comp., 62 (1994), pp. 179-207.
    • (1994) Math. Comp. , vol.62 , pp. 179-207
    • Ye, Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.