메뉴 건너뛰기




Volumn 432, Issue 8, 2010, Pages 1905-1922

On Newton's method and Halley's method for the principal pth root of a matrix

Author keywords

Convergence; H matrix; Halley's method; M matrix; Matrix pth root; Newton's method; Series expansion

Indexed keywords

H-MATRIX; HALLEY'S METHOD; M-MATRIX; MATRIX; NEWTON'S METHODS; PTH ROOTS; SERIES EXPANSION;

EID: 75749139718     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2009.02.030     Document Type: Article
Times cited : (40)

References (16)
  • 3
    • 0000954153 scopus 로고
    • A Schur method for the square root of a matrix
    • Björck A., and Hammarling S. 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
  • 4
    • 0041434416 scopus 로고
    • Analytic functions of M-matrices and generalizations
    • Fiedler M., and Schneider H. Analytic functions of M-matrices and generalizations. Linear and Multilinear Algebra 13 (1983) 185-201
    • (1983) Linear and Multilinear Algebra , vol.13 , pp. 185-201
    • Fiedler, M.1    Schneider, H.2
  • 5
    • 34547217286 scopus 로고    scopus 로고
    • A Schur-Newton method for the matrix pth root and its inverse
    • Guo C.-H., and Higham N.J. A Schur-Newton method for the matrix pth root and its inverse. SIAM J. Matrix Anal. Appl. 28 (2006) 788-804
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , pp. 788-804
    • Guo, C.-H.1    Higham, N.J.2
  • 6
    • 34547893797 scopus 로고    scopus 로고
    • Iterative solution of a nonsymmetric algebraic Riccati equation
    • Guo C.-H., and Higham N.J. Iterative solution of a nonsymmetric algebraic Riccati equation. SIAM J. Matrix Anal. Appl. 29 (2007) 396-412
    • (2007) SIAM J. Matrix Anal. Appl. , vol.29 , pp. 396-412
    • Guo, C.-H.1    Higham, N.J.2
  • 7
    • 0001485725 scopus 로고
    • Computing real square roots of a real matrix
    • Higham N.J. 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
  • 9
    • 34247403494 scopus 로고    scopus 로고
    • On the Newton method for the matrix pth root
    • Iannazzo B. On the Newton method for the matrix pth root. SIAM J. Matrix Anal. Appl. 28 (2006) 503-523
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , pp. 503-523
    • Iannazzo, B.1
  • 10
    • 70449133075 scopus 로고    scopus 로고
    • A family of rational iterations and its applications to the computation of the matrix pth root
    • Iannazzo B. A family of rational iterations and its applications to the computation of the matrix pth root. SIAM J. Matrix Anal. Appl. 30 (2008) 1445-1462
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , pp. 1445-1462
    • Iannazzo, B.1
  • 12
    • 21944450794 scopus 로고    scopus 로고
    • On the computation of the matrix k-th root
    • Lakić S. On the computation of the matrix k-th root. Z. Angew. Math. Mech. 78 (1998) 167-172
    • (1998) Z. Angew. Math. Mech. , vol.78 , pp. 167-172
    • Lakić, S.1
  • 13
    • 0035730407 scopus 로고    scopus 로고
    • On the square root of an H-matrix with positive diagonal elements
    • Lin L., and Liu Z.-Y. On the square root of an H-matrix with positive diagonal elements. Ann. Oper. Res. 103 (2001) 339-350
    • (2001) Ann. Oper. Res. , vol.103 , pp. 339-350
    • Lin, L.1    Liu, Z.-Y.2
  • 14
    • 17444381125 scopus 로고    scopus 로고
    • The matrix square root from a new functional perspective: Theoretical results and computational issues
    • Meini B. The matrix square root from a new functional perspective: Theoretical results and computational issues. SIAM J. Matrix Anal. Appl. 26 (2004) 362-376
    • (2004) SIAM J. Matrix Anal. Appl. , vol.26 , pp. 362-376
    • Meini, B.1
  • 15
    • 0142188203 scopus 로고    scopus 로고
    • A Schur algorithm for computing matrix pth roots
    • Smith M.I. A Schur algorithm for computing matrix pth roots. SIAM J. Matrix Anal. Appl. 24 (2003) 971-989
    • (2003) SIAM J. Matrix Anal. Appl. , vol.24 , pp. 971-989
    • Smith, M.I.1
  • 16
    • 34547202798 scopus 로고
    • Infinite product expansions for matrix n-th roots
    • Smith R.A. Infinite product expansions for matrix n-th roots. J. Austral. Math. Soc. 8 (1968) 242-249
    • (1968) J. Austral. Math. Soc. , vol.8 , pp. 242-249
    • Smith, R.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.