메뉴 건너뛰기




Volumn 22, Issue 4, 2001, Pages 1126-1135

Evaluating Padé approximants of the matrix logarithm

Author keywords

Continued fraction; Horner's method; Inverse scaling and squaring method; Matrix logarithm; Pad approximation; Partial fraction expansion; Paterson Stockmeyer method

Indexed keywords


EID: 0035537398     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479800368688     Document Type: Article
Times cited : (37)

References (19)
  • 2
    • 0000954153 scopus 로고
    • A Schur method for the square root of a matrix
    • A. BJÖRCK AND S. HAMMARLING, A Schur method for the square root of a matrix, Linear Algebra Appl., 52/53 (1983), pp. 127-140.
    • (1983) Linear Algebra Appl. , vol.52-53 , pp. 127-140
    • Björck, A.1    Hammarling, S.2
  • 3
    • 0001649757 scopus 로고
    • Numerical evaluation of continued fractions
    • G. BLANCH, Numerical evaluation of continued fractions, SIAM Rev., 6 (1964), pp. 383-421.
    • (1964) SIAM Rev. , vol.6 , pp. 383-421
    • Blanch, G.1
  • 4
    • 0029305258 scopus 로고
    • Incomplete partial fractions for parallel evaluation of rational matrix functions
    • D. CALVETTI, E GALLOPOULOS, AND L. REICHEL, Incomplete partial fractions for parallel evaluation of rational matrix functions, J. Comput. Appl. Math., 59 (1995), pp. 349-380.
    • (1995) J. Comput. Appl. Math. , vol.59 , pp. 349-380
    • Calvetti, D.1    Gallopoulos, E.2    Reichel, L.3
  • 7
    • 0030519907 scopus 로고    scopus 로고
    • Computational techniques for real logarithms of matrices
    • L. DIECI, B. MORINI, AND A. PAPINI, Computational techniques for real logarithms of matrices, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 570-593.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 570-593
    • Dieci, L.1    Morini, B.2    Papini, A.3
  • 8
    • 0028388229 scopus 로고
    • Algorithm 726: ORTHPOL - A package of routines for generating orthogonal polynomials and Gauss-type quadrature rules
    • W. GAUTSCHI, Algorithm 726: ORTHPOL - A package of routines for generating orthogonal polynomials and Gauss-type quadrature rules, ACM Trans. Math. Software, 20 (1994), pp. 21-62.
    • (1994) ACM Trans. Math. Software , vol.20 , pp. 21-62
    • Gautschi, W.1
  • 10
    • 0001485725 scopus 로고
    • Computing real square roots of a real matrix
    • N. J. HIGHAM, Computing real square roots of a real matrix, Linear Algebra Appl., 88/89 (1987), pp. 405-430.
    • (1987) Linear Algebra Appl. , vol.88-89 , pp. 405-430
    • Higham, N.J.1
  • 13
    • 0000831926 scopus 로고
    • Condition estimates for matrix functions
    • C. KENNEY AND A. J. LAUB, Condition estimates for matrix functions, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 191-209.
    • (1989) SIAM J. Matrix Anal. Appl. , vol.10 , pp. 191-209
    • Kenney, C.1    Laub, A.J.2
  • 14
    • 0024738860 scopus 로고
    • Padé error estimates for the logarithm of a matrix
    • C. KENNEY AND A. J. LAUB, Padé error estimates for the logarithm of a matrix, Internat. J. Control, 50 (1989), pp. 707-730.
    • (1989) Internat. J. Control , vol.50 , pp. 707-730
    • Kenney, C.1    Laub, A.J.2
  • 15
    • 0001143041 scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix
    • C. B. MOLER AND C. F. VAN LOAN, Nineteen dubious ways to compute the exponential of a matrix, SIAM Rev., 20 (1978), pp. 801-836.
    • (1978) SIAM Rev. , vol.20 , pp. 801-836
    • Moler, C.B.1    Van Loan, C.F.2
  • 16
    • 0002534227 scopus 로고
    • On the number of nonscalar multiplications necessary to evaluate polynomials
    • M. S. PATERSON AND L. J. STOCKMEYER, On the number of nonscalar multiplications necessary to evaluate polynomials, SIAM J. Comput., 2 (1973), pp. 60-66.
    • (1973) SIAM J. Comput. , vol.2 , pp. 60-66
    • Paterson, M.S.1    Stockmeyer, L.J.2
  • 18
    • 0001259715 scopus 로고
    • A note on the evaluation of matrix polynomials
    • C. F. VAN LOAN, A note on the evaluation of matrix polynomials, IEEE Trans. Automat. Control, AC-24 (1979), pp. 320-321.
    • (1979) IEEE Trans. Automat. Control , vol.AC-24 , pp. 320-321
    • Van Loan, C.F.1
  • 19
    • 0001332750 scopus 로고
    • Numerical computation of the matrix exponential with accuracy estimate
    • R. C. WARD, Numerical computation of the matrix exponential with accuracy estimate, SIAM J. Numer. Anal., 14 (1977), pp. 600-610.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 600-610
    • Ward, R.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.