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Volumn 12, Issue 7, 2005, Pages 625-658

An implicit QR algorithm for symmetric semiseparable matrices

Author keywords

Eigenvalues; Eigenvectors; Implicit QR algorithm for semiseparable matrices; Semiseparable matrix; Similarity reduction to semiseparable form; Symmetric matrix

Indexed keywords


EID: 25144442638     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.425     Document Type: Article
Times cited : (30)

References (38)
  • 3
    • 0031082738 scopus 로고    scopus 로고
    • A fast adaptive numerical method for stiff two-point boundary value problems
    • Lee J-Y, Greengard L. A fast adaptive numerical method for stiff two-point boundary value problems. SIAM Journal on Scientific Computing 1997; 18(2):403-429.
    • (1997) SIAM Journal on Scientific Computing , vol.18 , Issue.2 , pp. 403-429
    • Lee, J.-Y.1    Greengard, L.2
  • 10
    • 0000785766 scopus 로고
    • Time varying linear systems with boundary conditions and integral operators, I. The transfer operator and its properties
    • Gohberg I, Kaashoek MA. Time varying linear systems with boundary conditions and integral operators, I. The transfer operator and its properties. Integral Equations and Operator Theory 1984; 7:325-391.
    • (1984) Integral Equations and Operator Theory , vol.7 , pp. 325-391
    • Gohberg, I.1    Kaashoek, M.A.2
  • 11
    • 0013293393 scopus 로고    scopus 로고
    • A Lanczos type algorithm for the QR-factorization of regular Cauchy matrices
    • Fasino D, Gemignani L. A Lanczos type algorithm for the QR-factorization of regular Cauchy matrices. Numerical Linear Algebra with Applications 2002; 9:305-319.
    • (2002) Numerical Linear Algebra with Applications , vol.9 , pp. 305-319
    • Fasino, D.1    Gemignani, L.2
  • 12
    • 4043086344 scopus 로고    scopus 로고
    • Direct and inverse eigenvalue problems, for diagonal-plus-semiseparable matrices
    • Fasino D, Gemignani L. Direct and inverse eigenvalue problems, for diagonal-plus-semiseparable matrices. Numerical Algorithms 2003; 34:313-324.
    • (2003) Numerical Algorithms , vol.34 , pp. 313-324
    • Fasino, D.1    Gemignani, L.2
  • 15
    • 0034224295 scopus 로고    scopus 로고
    • Matrices with banded inverses: Inversion algorithms and factorization of Gauss-Markov processes
    • Kavčič A, Moura MF. Matrices with banded inverses: inversion algorithms and factorization of Gauss-Markov processes. IEEE Transactions on Information Theory 2000; 46(4):1495-1509.
    • (2000) IEEE Transactions on Information Theory , vol.46 , Issue.4 , pp. 1495-1509
    • Kavčič, A.1    Moura, M.F.2
  • 20
    • 21344495471 scopus 로고
    • Iteration schemes for the divide-and-conquer eigenvalue solver
    • Bini DA, Gemignani L. Iteration schemes for the divide-and-conquer eigenvalue solver. Numerische Mathematik 1994; 67:403-425.
    • (1994) Numerische Mathematik , vol.67 , pp. 403-425
    • Bini, D.A.1    Gemignani, L.2
  • 21
    • 0039923684 scopus 로고
    • A parallel divide and conquer algorithm for the generalized real symmetric definite tridiagonal eigenproblem
    • Borges CF, Gragg WB. A parallel divide and conquer algorithm for the generalized real symmetric definite tridiagonal eigenproblem. Numerical Linear Algebra (Kent, OH, 1992) 1993; 11-29.
    • (1993) Numerical Linear Algebra (Kent, OH, 1992) , pp. 11-29
    • Borges, C.F.1    Gragg, W.B.2
  • 22
    • 0000659575 scopus 로고
    • A divide and conquer method for the symmetric tridiagonal eigenproblem
    • Cuppen JJM. A divide and conquer method for the symmetric tridiagonal eigenproblem. Numerische Mathematik 1981; 36:177-195.
    • (1981) Numerische Mathematik , vol.36 , pp. 177-195
    • Cuppen, J.J.M.1
  • 24
    • 1542403825 scopus 로고    scopus 로고
    • A divide and conquer algorithm for the eigendecomposition of symmetric block-diagonal plus semi-separable matrices
    • Chandrasekaran S, Gu M. A divide and conquer algorithm for the eigendecomposition of symmetric block-diagonal plus semi-separable matrices. Numerische Mathematik 2004; 96(4):723-731.
    • (2004) Numerische Mathematik , vol.96 , Issue.4 , pp. 723-731
    • Chandrasekaran, S.1    Gu, M.2
  • 25
    • 20344372250 scopus 로고    scopus 로고
    • Fast and stable algorithms for reducing diagonal plus semi-separable matrices to tridiagonal and bidiagonal form
    • Fasino D, Mastronardi N, Van Barel M. Fast and stable algorithms for reducing diagonal plus semi-separable matrices to tridiagonal and bidiagonal form. Contemporary Mathematics 2003; 323:105-119.
    • (2003) Contemporary Mathematics , vol.323 , pp. 105-119
    • Fasino, D.1    Mastronardi, N.2    Van Barel, M.3
  • 26
    • 0013420838 scopus 로고    scopus 로고
    • Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form
    • Mastronardi N, Chandrasekaran S, Van Huffel S. Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form. BIT 2003; 41(1): 149-157.
    • (2003) BIT , vol.41 , Issue.1 , pp. 149-157
    • Mastronardi, N.1    Chandrasekaran, S.2    Van Huffel, S.3
  • 28
    • 0034394306 scopus 로고    scopus 로고
    • Fast and stable eigendecomposition of symmetric banded plus semi-separable matrices
    • Chandrasekaran S, Gu M. Fast and stable eigendecomposition of symmetric banded plus semi-separable matrices. Linear Algebra and its Applications 2000; 313:107-114.
    • (2000) Linear Algebra and Its Applications , vol.313 , pp. 107-114
    • Chandrasekaran, S.1    Gu, M.2
  • 30
    • 0032395502 scopus 로고    scopus 로고
    • Reliable computation of the condition number of a tridiagonal matrix in O(n) time
    • Dhillon IS. Reliable computation of the condition number of a tridiagonal matrix in O(n) time. SIAM Journal on Matrix Analysis and its Applications 1998; 19(3):776-796.
    • (1998) SIAM Journal on Matrix Analysis and Its Applications , vol.19 , Issue.3 , pp. 776-796
    • Dhillon, I.S.1
  • 32
    • 11144294629 scopus 로고    scopus 로고
    • QR-like algorithms for generalized semiseparable matrices
    • Department of Mathematics, University of Pisa
    • Bini DA, Gemignani L, Pan V. QR-like algorithms for generalized semiseparable matrices. Technical Report 1470, Department of Mathematics, University of Pisa, 2004.
    • (2004) Technical Report , vol.1470
    • Bini, D.A.1    Gemignani, L.2    Pan, V.3
  • 34
    • 21344478071 scopus 로고
    • Theory of decomposition and bulge-chasing algorithms for the generalized eigenvalue problem
    • Watkins DS, Elsner L. Theory of decomposition and bulge-chasing algorithms for the generalized eigenvalue problem. SIAM Journal on Matrix Analysis and its Applications 1994; 15(3):943-967.
    • (1994) SIAM Journal on Matrix Analysis and Its Applications , vol.15 , Issue.3 , pp. 943-967
    • Watkins, D.S.1    Elsner, L.2
  • 35
    • 0037532899 scopus 로고    scopus 로고
    • Some algorithms for solving special tridiagonal block toeplitz linear systems
    • Minchev BV. Some algorithms for solving special tridiagonal block toeplitz linear systems. Journal of Computational and Applied Mathematics 2003; 156:179-200.
    • (2003) Journal of Computational and Applied Mathematics , vol.156 , pp. 179-200
    • Minchev, B.V.1
  • 36
    • 12944291125 scopus 로고    scopus 로고
    • Existence, uniqueness and algorithms for matrix unitary reduction to semiseparable form
    • University of Pisa, July
    • Bevilacqua R, Del Corso GM. Existence, uniqueness and algorithms for matrix unitary reduction to semiseparable form. Technical Report TR-03-12, University of Pisa, July 2003.
    • (2003) Technical Report , vol.TR-03-12
    • Bevilacqua, R.1    Del Corso, G.M.2
  • 37
    • 0003358142 scopus 로고    scopus 로고
    • The symmetric eigenvalue problem
    • SIAM: Philadelphia, PA
    • Parlett BN. The symmetric eigenvalue problem. Classics in Applied Mathematics, vol. 20. SIAM: Philadelphia, PA, 1998.
    • (1998) Classics in Applied Mathematics , vol.20
    • Parlett, B.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.