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Volumn 31, Issue , 2008, Pages 358-383

Algorithms for the matrix sector function

Author keywords

Conditioning; Frechet derivative; Halley'S method; Matrix pth root; Matrix sector function; Matrix sign function; Newton'S method; Parlett recurrence; Schur algorithm; Stability

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; NATURAL GAS CONDITIONING; NEWTON-RAPHSON METHOD;

EID: 70449128550     PISSN: None     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (10)

References (20)
  • 1
    • 70449440430 scopus 로고    scopus 로고
    • Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation
    • A. H. Al-Mohy and N. J. Higham, Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation, SIAM J. Matrix Anal. Appl., 30 (2009), pp. 1639-1657.
    • (2009) SIAM J. Matrix Anal. Appl. , vol.30 , pp. 1639-1657
    • Al-Mohy, A.H.1    Higham, N.J.2
  • 2
    • 17544381599 scopus 로고    scopus 로고
    • Algorithms for the matrix pth root
    • D. A. Bini, N. J. Higham, and B. Meini, Algorithms for the matrix pth root, Numer. Algorithms, 39 (2005), pp. 349-378.
    • (2005) Numer. Algorithms , vol.39 , pp. 349-378
    • Bini, D.A.1    Higham, N.J.2    Meini, B.3
  • 3
    • 1842865578 scopus 로고    scopus 로고
    • A Schur-Parlett algorithm for computing matrix functions
    • P. I. Davies and N. J. Higham, A Schur-Parlett algorithm for computing matrix functions, SIAM J. Matrix Anal. Appl., 25 (2003), pp. 464-485.
    • (2003) SIAM J. Matrix Anal. Appl. , vol.25 , pp. 464-485
    • Davies, P.I.1    Higham, N.J.2
  • 4
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed., Johns Hopkins University Press, Baltimore
    • G. H. Golub and C. F. Van Loan, Matrix Computation, 3rd ed., Johns Hopkins University Press, Baltimore, 1996.
    • (1996) Matrix Computation
    • Golub, G.H.1    Van Loan, C.F.2
  • 5
    • 34547217286 scopus 로고    scopus 로고
    • A Schur-Newton method for the matrix pth root and its inverse
    • Ch.-H. Guo and N. J. Higham, A Schur-Newton method for the matrix pth root and its inverse, SIAM J. Matrix Anal. Appl., 28 (2006), pp. 788-804.
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , pp. 788-804
    • Guo, Ch.-H.1    Higham, N.J.2
  • 6
    • 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)PP.3-20.
    • (1994) Linear Algebra Appl. , vol.212-213 , pp. 3-20
    • Higham, N.J.1
  • 7
    • 70449395396 scopus 로고    scopus 로고
    • Functions ofMatrices: Theory and Computations
    • Philadelphia
    • N. J. Higham, Functions ofMatrices: Theory and Computations, SIAM, Philadelphia, 2008.
    • (2008) SIAM
    • Higham, N.J.1
  • 8
    • 8344275080 scopus 로고    scopus 로고
    • Computing the polar decomposition and the matrix sign decomposition in matrix groups
    • N. J. Higham, D. S. Mackey, N. Mackey, and F. Tisseur, Computing the polar decomposition and the matrix sign decomposition in matrix groups, SIAM J. Matrix Anal. Appl., 25 (2004), pp. 1178-1192.
    • (2004) SIAM J. Matrix Anal. Appl. , vol.25 , pp. 1178-1192
    • Higham, N.J.1    Mackey, D.S.2    Mackey, N.3    Tisseur, F.4
  • 9
    • 34247403494 scopus 로고    scopus 로고
    • On the Newton method for the matrix pth root
    • N. J. Higham, The matrix sign decomposition and its relation to the polar decomposition, Linear Algebra Appl., 212/213 (1994), pp. 320.
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , pp. 503-523
    • Iannazzo, B.1
  • 10
    • 70449101771 scopus 로고    scopus 로고
    • Numerical solution of certain nonlinear matrix equations
    • Universita degli Studi di Pisa, Facolta di Scienze Matematiche, Fisiche e Naturali
    • B. Iannazzo, Numerical solution of certain nonlinear matrix equations, Ph.D. thesis, Universita degli Studi di Pisa, Facolta di Scienze Matematiche, Fisiche e Naturali,2007.
    • (2007) Ph.D. thesis
    • Iannazzo, B.1
  • 11
    • 70449133075 scopus 로고    scopus 로고
    • A family of rational iterations and its application to the computation ofthe matrix pth root
    • B. Iannazzo, A family of rational iterations and its application to the computation ofthe matrix pth root, SIAM J. Matrix Anal. Appl., 30 (2008), pp.144-51462.
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , pp. 144-51462
    • Iannazzo, B.1
  • 12
    • 0001537596 scopus 로고
    • Polar decomposition and matrix sign function condition estimates
    • Ch. Kenney and A. J. Laub, Polar decomposition and matrix sign function condition estimates, SIAM J. Sci. Stat. Comput., 12 (1991), pp. 488-504.
    • (1991) SIAM J. Sci. Stat. Comput. , vol.12 , pp. 488-504
    • Kenney, Ch.1    Laub, A.J.2
  • 13
    • 0029304771 scopus 로고
    • Halley method for the matrix sector function
    • C. K. Koc and B. Bakkaloglu, Halley method for the matrix sector function, IEEE Trans. Automat. Control, 40 (1995), pp. 944-949.
    • (1995) IEEE Trans. Automat. Control , vol.40 , pp. 944-949
    • Koc, C.K.1    Bakkaloglu, B.2
  • 14
    • 70449120332 scopus 로고    scopus 로고
    • The Padé family of iterations for the matrix sector function and the matrix pth root, To appear in Numer
    • B. Laszkiewicz and K. Ziijtak, The Padé family ofiterations for the matrix sector function and the matrix pth root, To appear in Numer. Linear Algebra Appl., 2009.
    • (2009) Linear Algebra Appl.
    • Laszkiewicz, B.1    Ziijtak, K.2
  • 15
    • 0030519908 scopus 로고    scopus 로고
    • A chain rule for matrix functions and applications
    • R. Mathias, A chain rule for matrix functions and applications, SIAM J. Matrix Anal. Appl.,17 (1996), pp. 610-620.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 610-620
    • R. Mathias1
  • 16
    • 0000312029 scopus 로고
    • A reccurence among the elements offunctions oftriangular matrices
    • B. N. Parlett, A reccurence among the elements offunctions oftriangular matrices, Linear Algebra Appl., 14 (1976), pp. 117-121.
    • (1976) Linear Algebra Appl. , vol.14 , pp. 117-121
    • B.N. Parlett1
  • 17
    • 0019069037 scopus 로고
    • Linear model reduction and solution ofthe algebraic Riccati equation by use ofthe sign function, Internat
    • J. D. Roberts, Linear model reduction and solution ofthe algebraic Riccati equation by use ofthe sign function, Internat. J. Control, 32 (1980), pp. 677-687.
    • (1980) J. Control , vol.32 , pp. 677-687
    • J.D. Roberts1
  • 18
    • 0021496786 scopus 로고
    • Matrix sector functions and their applications to systems theory
    • L. S. Shieh, Y. T. Tsay, And C. T. Wang, Matrix sector functions and their applications to systems theory, IEEE Proc. 131 (1984), pp. 171-181.
    • (1984) IEEE Proc. , vol.131 , pp. 171-181
    • Shieh, L.S.1    Tsay, Y.T.2    Wang, C.T.3
  • 19
    • 72449129377 scopus 로고    scopus 로고
    • Ph.D. thesis, University of Manchester, Faculty of Science and Engineering, Department of Mathematics
    • M. I. Smith, Numerical Computation of Matrix Functions, Ph.D. thesis, University of Manchester, Faculty of Science and Engineering, Department of Mathematics, 2002.
    • (2002) Numerical Computation of Matrix Functions
    • M.I. Smith1
  • 20
    • 0142188203 scopus 로고    scopus 로고
    • A Schur algorithm for computing matrix pth root
    • M. I. Smith, A Schur algorithm for computing matrix pth root, SIAM J. Matrix Anal. Appl., 24 (2003), pp. 971-989.
    • (2003) SIAM J. Matrix Anal. Appl. , vol.24 , pp. 971-989
    • M.I. Smith1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.