메뉴 건너뛰기




Volumn 21, Issue 4, 2000, Pages 1185-1201

A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra

Author keywords

1 norm pseudospectrum; Condition number estimation; LAPACK; Level 3 BLAS; Matrix 1 norm; Matrix condition number; Matrix norm estimation; p norm power method

Indexed keywords


EID: 0034144755     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479899356080     Document Type: Article
Times cited : (117)

References (22)
  • 2
    • 0000015959 scopus 로고
    • Solving sparse linear systems with sparse backward error
    • M. ARIOLI, J. W. DEMMEL, AND I. S. DUFF, Solving sparse linear systems with sparse backward error, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 165-190.
    • (1989) SIAM J. Matrix Anal. Appl. , vol.10 , pp. 165-190
    • Arioli, M.1    Demmel, J.W.2    Duff, I.S.3
  • 5
    • 0001511322 scopus 로고
    • A set of counter-examples to three condition number estimators
    • A. K. CLINE AND R. K. REW, A set of counter-examples to three condition number estimators, SIAM J. Sci. Stat. Comput., 4 (1983), pp. 602-611.
    • (1983) SIAM J. Sci. Stat. Comput. , vol.4 , pp. 602-611
    • Cline, A.K.1    Rew, R.K.2
  • 6
    • 0001820070 scopus 로고
    • IMA Preprint Series #961, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN
    • J. W. DEMMEL, Open Problems in Numerical Linear Algebra, IMA Preprint Series #961, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN, 1992.
    • (1992) Open Problems in Numerical Linear Algebra
    • Demmel, J.W.1
  • 7
    • 0001290746 scopus 로고
    • Estimating extremal eigenvalues and condition numbers of matrices
    • J. D. DIXON, Estimating extremal eigenvalues and condition numbers of matrices, SIAM J. Numer. Anal., 20 (1983), pp. 812-814.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 812-814
    • Dixon, J.D.1
  • 10
    • 0000426239 scopus 로고
    • A stable variant of the secant method for solving nonlinear equations
    • W. B. GRAGG AND G. W. STEWART, A stable variant of the secant method for solving nonlinear equations, SIAM J. Numer. Anal., 13 (1976), pp. 889-903.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 889-903
    • Gragg, W.B.1    Stewart, G.W.2
  • 13
    • 0023538126 scopus 로고
    • A survey of condition number estimation for triangular matrices
    • N. J. HIGHAM, A survey of condition number estimation for triangular matrices, SIAM Rev., 29 (1987), pp. 575-596.
    • (1987) SIAM Rev. , vol.29 , pp. 575-596
    • Higham, N.J.1
  • 14
    • 0024143903 scopus 로고
    • FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation (Algorithm 674)
    • N. J. HIGHAM, FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation (Algorithm 674), ACM Trans. Math. Software, 14 (1988), pp. 381-396.
    • (1988) ACM Trans. Math. Software , vol.14 , pp. 381-396
    • Higham, N.J.1
  • 15
    • 0000300384 scopus 로고
    • Experience with a matrix norm estimator
    • N. J. HIGHAM, Experience with a matrix norm estimator, SIAM J. Sci. Stat. Comput., 11 (1990), pp. 804-809.
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , pp. 804-809
    • Higham, N.J.1
  • 17
    • 0001967018 scopus 로고    scopus 로고
    • A numerical analyst looks at the "cutoff phenomenon" in card shuffling and other markov chains
    • Numerical Analysis 1997, Proceedings of the 17th Dundee Biennial Conference, D. F. Griffiths, D. J. Higham, and G. A. Watson, eds., Addison Wesley Longman, Harlow, Essex, UK
    • G. F. JÓNSSON AND L. N. TREFETHEN, A numerical analyst looks at the "cutoff phenomenon" in card shuffling and other Markov chains, in Numerical Analysis 1997, Proceedings of the 17th Dundee Biennial Conference, D. F. Griffiths, D. J. Higham, and G. A. Watson, eds., Pitman Res. Notes Math. Ser. 380, Addison Wesley Longman, Harlow, Essex, UK, 1998, pp. 150-178.
    • (1998) Pitman Res. Notes Math. Ser. , vol.380 , pp. 150-178
    • Jónsson, G.F.1    Trefethen, L.N.2
  • 18
    • 0001861849 scopus 로고
    • Convergence of a subgradient method for computing the bound norm of matrices
    • in French
    • P. D. TAO, Convergence of a subgradient method for computing the bound norm of matrices, Linear Algebra Appl., 62 (1984), pp. 163-182 (in French).
    • (1984) Linear Algebra Appl. , vol.62 , pp. 163-182
    • Tao, P.D.1
  • 19
    • 0000992781 scopus 로고
    • Pseudospectra of matrices
    • Numerical Analysis 1991, Proceedings of the 14th Dundee Conference, D. F. Griffiths and G. A. Watson, eds., Longman Scientific and Technical, Essex, UK
    • L. N. TREFETHEN, Pseudospectra of matrices, in Numerical Analysis 1991, Proceedings of the 14th Dundee Conference, D. F. Griffiths and G. A. Watson, eds., Pitman Res. Notes Math. 260, Longman Scientific and Technical, Essex, UK, 1992, pp. 234-266.
    • (1992) Pitman Res. Notes Math. , vol.260 , pp. 234-266
    • Trefethen, L.N.1
  • 20
    • 0031238062 scopus 로고    scopus 로고
    • Pseudospectra of linear operators
    • L. N. TREFETHEN, Pseudospectra of linear operators, SIAM Rev., 39 (1997), pp. 383-406.
    • (1997) SIAM Rev. , vol.39 , pp. 383-406
    • Trefethen, L.N.1
  • 21
    • 85011519633 scopus 로고    scopus 로고
    • Computation of pseudospectra
    • A. Iseries, ed., Cambridge University Press, Cambridge, UK
    • L. N. TREFETHEN, Computation of pseudospectra, in Acta Numerica 8, A. Iseries, ed., Cambridge University Press, Cambridge, UK, 1999, pp. 247-295.
    • (1999) Acta Numerica , vol.8 , pp. 247-295
    • Trefethen, L.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.