메뉴 건너뛰기




Volumn 15, Issue 2, 1997, Pages 227-242

Stable iterations for the matrix square root

Author keywords

M matrix; Matrix logarithm; Matrix sign function; Matrix square root; Newton's method; Numerical stability; Pad approximation; Schulz method; Symmetric positive definite matrix

Indexed keywords


EID: 21944447246     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1019150005407     Document Type: Article
Times cited : (184)

References (18)
  • 3
    • 0003658403 scopus 로고
    • Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, first published 1979 by Academic Press
    • A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences (Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1994; first published 1979 by Academic Press).
    • (1994) Nonnegative Matrices in the Mathematical Sciences
    • Berman, A.1    Plemmons, R.J.2
  • 4
    • 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) 127-140.
    • (1983) Linear Algebra Appl. , vol.52-53 , pp. 127-140
    • Björck, A.1    Hammarling, S.2
  • 5
    • 27144514233 scopus 로고
    • Nonnegative solutions of a quadratic matrix equation arising from comparison theorems in ordinary differential equations
    • G.J. Butler, C.R. Johnson and H. Wolkowicz, Nonnegative solutions of a quadratic matrix equation arising from comparison theorems in ordinary differential equations, SIAM J. Alg. Disc. Meth. 6(1) (1985) 47-53.
    • (1985) SIAM J. Alg. Disc. Meth. , vol.6 , Issue.1 , pp. 47-53
    • Butler, G.J.1    Johnson, C.R.2    Wolkowicz, H.3
  • 6
    • 38249038136 scopus 로고
    • Solving the algebraic Riccati equation with the matrix sign function
    • R. Byers, Solving the algebraic Riccati equation with the matrix sign function, Linear Algebra Appl. 85 (1987) 267-279.
    • (1987) Linear Algebra Appl. , vol.85 , pp. 267-279
    • Byers, R.1
  • 8
    • 0002656851 scopus 로고
    • The matrix sign function and computations in systems
    • L.D. Denman and A.N. Beavers, Jr., The matrix sign function and computations in systems, Appl. Math. Comput. 2 (1976) 63-94.
    • (1976) Appl. Math. Comput. , vol.2 , pp. 63-94
    • Denman, L.D.1    Beavers Jr., A.N.2
  • 9
    • 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(3) (1996) 570-593.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , Issue.3 , pp. 570-593
    • Dieci, L.1    Morini, B.2    Papini, A.3
  • 10
    • 0004236492 scopus 로고    scopus 로고
    • Johns Hopkins Univ. Press, 3rd ed., Baltimore, MD, USA
    • G.H. Golub and C.F. Van Loan, Matrix Computations (Johns Hopkins Univ. Press, 3rd ed., Baltimore, MD, USA, 1996).
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 12
    • 0001692403 scopus 로고
    • Computing the polar decomposition - With applications
    • N.J. Higham, Computing the polar decomposition - with applications, SIAM J. Sci. Statist. Comput. 7(4) (1986) 1160-1174.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , Issue.4 , pp. 1160-1174
    • Higham, N.J.1
  • 13
    • 0001301897 scopus 로고
    • Newton's method for the matrix square root
    • N.J. Higham, Newton's method for the matrix square root, Math. Comp. 46(174) (1986) 537-549.
    • (1986) Math. Comp. , vol.46 , Issue.174 , pp. 537-549
    • Higham, N.J.1
  • 14
    • 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) 405-430.
    • (1987) Linear Algebra Appl. , vol.88-89 , pp. 405-430
    • Higham, N.J.1
  • 15
    • 0003492388 scopus 로고
    • The Test Matrix Toolbox for Matlab (version 3.0)
    • Manchester Centre for Computational Mathematics, Manchester, England, September
    • N.J. Higham, The Test Matrix Toolbox for Matlab (version 3.0), Numerical Analysis Report No. 276, Manchester Centre for Computational Mathematics, Manchester, England, September (1995) 70 pp.
    • (1995) Numerical Analysis Report No. 276 , vol.276
    • Higham, N.J.1
  • 16
    • 0348188053 scopus 로고
    • The matrix sign decomposition and its relation to the polar decomposition
    • N.J. Higham, The matrix sign decomposition and its relation to the polar decomposition, Linear Algebra Appl. 212/213 (1994) 3-20.
    • (1994) Linear Algebra Appl. , vol.212-213 , pp. 3-20
    • Higham, N.J.1
  • 18
    • 0028480593 scopus 로고
    • A parallel algorithm for computing the polar decomposition
    • N.J. Higham and P. Papadimitriou, A parallel algorithm for computing the polar decomposition, Parallel Comput. 20(8) (1994) 1161-1173.
    • (1994) Parallel Comput. , vol.20 , Issue.8 , pp. 1161-1173
    • Higham, N.J.1    Papadimitriou, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.