메뉴 건너뛰기




Volumn 35, Issue 2, 2013, Pages

A framework for the MR3 algorithm: Theory and implementation

Author keywords

Eigensystem; MRRR algorithm; Symmetric tridiagonal matrix; Theory and implementation

Indexed keywords

COMPUTATION THEORY; LINEAR TRANSFORMATIONS;

EID: 84880609263     PISSN: 10648275     EISSN: 10957200     Source Type: Journal    
DOI: 10.1137/110834020     Document Type: Article
Times cited : (8)

References (39)
  • 2
    • 33144474872 scopus 로고    scopus 로고
    • A parallel eigensolver for dense symmetric matrices based on multiple relatively robust representations
    • P. BIENTINESI, I. S. DHILLON, AND R. A. VAN DE GEIJN, A parallel eigensolver for dense symmetric matrices based on multiple relatively robust representations, SIAM J. Sci. Comput., 27(2005), pp. 43-66.
    • (2005) SIAM J. Sci. Comput. , vol.27 , pp. 43-66
    • Bientinesi, P.1    Dhillon, I.S.2    Van De Geijn, R.A.3
  • 3
    • 0000659575 scopus 로고
    • A divide and conquer method for the symmetric tridiagonal eigenproblem
    • J. J. M. CUPPEN, A divide and conquer method for the symmetric tridiagonal eigenproblem, Numer. Math., 36(1981), pp. 177-195.
    • (1981) Numer. Math. , vol.36 , pp. 177-195
    • Cuppen, J.J.M.1
  • 5
    • 0001192187 scopus 로고
    • Accurate singular values of bidiagonal matrices
    • J. W. DEMMEL AND W. KAHAN, Accurate singular values of bidiagonal matrices, SIAM J. Sci. Comput., 11(1990), pp. 873-912.
    • (1990) SIAM J. Sci. Comput. , vol.11 , pp. 873-912
    • Demmel, J.W.1    Kahan, W.2
  • 6
    • 55549110811 scopus 로고    scopus 로고
    • Performance and accuracy of LAPACK's symmetric tridiagonal eigensolvers
    • J. W. DEMMEL, O. A. MARQUES, B. N. PARLETT, AND C. VÖMEL, Performance and accuracy of LAPACK's symmetric tridiagonal eigensolvers, SIAM J. Sci. Comput., 30(2008), pp. 1508-1526.
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 1508-1526
    • Demmel, J.W.1    Marques, O.A.2    Parlett, B.N.3    Vömel, C.4
  • 8
    • 2942522546 scopus 로고    scopus 로고
    • Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices
    • I. S. DHILLON AND B. N. PARLETT, Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices, Linear Algebra Appl., 387(2004), pp. 1-28.
    • (2004) Linear Algebra Appl. , vol.387 , pp. 1-28
    • Dhillon, I.S.1    Parlett, B.N.2
  • 9
  • 11
  • 12
    • 0031536846 scopus 로고    scopus 로고
    • On computing an eigenvector of a tridiagonal matrix. Part I: Basic results
    • K. V. FERNANDO, On computing an eigenvector of a tridiagonal matrix. Part I: Basic results, SIAM J. Matrix Anal. Appl., 18(1997), pp. 1013-1034.
    • (1997) SIAM J. Matrix Anal. Appl. , vol.18 , pp. 1013-1034
    • Fernando, K.V.1
  • 13
    • 21344496407 scopus 로고
    • Accurate singular values and differential qd algorithms
    • K. V. FERNANDO AND B. N. PARLETT, Accurate singular values and differential qd algorithms, Numer. Math., 67(1994), pp. 191-229.
    • (1994) Numer. Math. , vol.67 , pp. 191-229
    • Fernando, K.V.1    Parlett, B.N.2
  • 14
    • 0000394782 scopus 로고
    • The QR transformation: A unitary analogue to the LR transformation. I
    • J. FRANCIS, The QR transformation: A unitary analogue to the LR transformation. I., Comput. J., 4(1961/1962), pp. 265-271.
    • (1961) Comput. J. , vol.4 , pp. 265-271
    • Francis, J.1
  • 15
    • 0000394779 scopus 로고
    • The QR transformation. II
    • J. FRANCIS, The QR transformation. II., Comput. J., 4(1961/1962), pp. 332-345.
    • (1961) Comput. J. , vol.4 , pp. 332-345
    • Francis, J.1
  • 16
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed., Johns Hopkins University Press, Baltimore, MD
    • G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996.
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 17
    • 22944481788 scopus 로고    scopus 로고
    • Ph. D. thesis, Bergische Universität Gesamthochschule Wuppertal, Fachbereich Mathematik, Wuppertal, Germany
    • 2) Algorithmus für die bidiagonale Singulärwertzerlegung, Ph. D. thesis, Bergische Universität Gesamthochschule Wuppertal, Fachbereich Mathematik, Wuppertal, Germany, 2001.
    • (2001) 2) Algorithmus für die Bidiagonale Singulärwertzerlegung
    • Großer, B.1
  • 18
    • 21844526695 scopus 로고
    • A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem
    • M. GU AND S. C. EISENSTAT, A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem, SIAM J. Matrix Anal. Appl., 16(1995), pp. 172-191.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 172-191
    • Gu, M.1    Eisenstat, S.C.2
  • 19
    • 0031166040 scopus 로고    scopus 로고
    • Computing an eigenvector with inverse iteration
    • I. C. F. IPSEN, Computing an eigenvector with inverse iteration, SIAM Rev., 39(1997), pp. 254-291.
    • (1997) SIAM Rev. , vol.39 , pp. 254-291
    • Ipsen, I.C.F.1
  • 20
    • 0004222768 scopus 로고
    • Technical Report CS41, Computer Science Department, Stanford University, Stanford, CA
    • W. KAHAN, Accurate Eigenvalues of a Symmetric Tri-diagonal Matrix, Technical Report CS41, Computer Science Department, Stanford University, Stanford, CA, 1966.
    • (1966) Accurate Eigenvalues of a Symmetric Tri-diagonal Matrix
    • Kahan, W.1
  • 21
    • 0011040261 scopus 로고    scopus 로고
    • Using level 3 BLAS in rotation-based algorithms
    • B. LANG, Using level 3 BLAS in rotation-based algorithms, SIAM J. Sci. Comput., 19(1998), pp. 626-634.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 626-634
    • Lang, B.1
  • 22
    • 33749327597 scopus 로고    scopus 로고
    • Computations of eigenpair subsets with the MRRR algorithm
    • O. A. MARQUES, B. N. PARLETT, AND C. VÖMEL, Computations of eigenpair subsets with the MRRR algorithm, Numer. Linear Algebra Appl., 13(2006), pp. 643-653.
    • (2006) Numer. Linear Algebra Appl. , vol.13 , pp. 643-653
    • Marques, O.A.1    Parlett, B.N.2    Vömel, C.3
  • 23
    • 48849105175 scopus 로고    scopus 로고
    • Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers
    • O. A. MARQUES, C. VÖMEL, J. W. DEMMEL, AND B. N. PARLETT, Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers, ACM Trans. Math. Software, 35(2008), pp. 8:1-8:13.
    • (2008) ACM Trans. Math. Software , vol.35 , pp. 81-813
    • Marques, O.A.1    Vömel, C.2    Demmel, J.W.3    Parlett, B.N.4
  • 25
    • 0039329962 scopus 로고    scopus 로고
    • Invariant subspaces for tightly clustered eigenvalues of tridiagonals
    • B. N. PARLETT, Invariant subspaces for tightly clustered eigenvalues of tridiagonals, BIT, 36(1996), pp. 542-562.
    • (1996) BIT , vol.36 , pp. 542-562
    • Parlett, B.N.1
  • 26
    • 0032390277 scopus 로고    scopus 로고
    • Spectral sensitivity of products of bidiagonals
    • B. N. PARLETT, Spectral sensitivity of products of bidiagonals, Linear Algebra Appl., 275/276(1998), pp. 417-431.
    • (1998) Linear Algebra Appl. , vol.275-276 , pp. 417-431
    • Parlett, B.N.1
  • 27
    • 26044479495 scopus 로고    scopus 로고
    • Perturbation of eigenpairs of factored symmetric tridiagonal matrices
    • B. N. PARLETT, Perturbation of eigenpairs of factored symmetric tridiagonal matrices, Found. Comput. Math., 3(2003), pp. 207-223.
    • (2003) Found. Comput. Math. , vol.3 , pp. 207-223
    • Parlett, B.N.1
  • 28
    • 27144543771 scopus 로고    scopus 로고
    • A bidiagonal matrix determines its hyperbolic SVD to varied relative accuracy
    • B. N. PARLETT, A bidiagonal matrix determines its hyperbolic SVD to varied relative accuracy, SIAM J. Matrix Anal. Appl., 26(2005), pp. 1022-1057.
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , pp. 1022-1057
    • Parlett, B.N.1
  • 29
    • 0039504477 scopus 로고    scopus 로고
    • Fernando's solution to Wilkinson's problem: An application of double factorization
    • B. N. PARLETT AND I. S. DHILLON, Fernando's solution to Wilkinson's problem: An application of double factorization, Linear Algebra Appl., 267(1997), pp. 247-279.
    • (1997) Linear Algebra Appl. , vol.267 , pp. 247-279
    • Parlett, B.N.1    Dhillon, I.S.2
  • 30
    • 0034421232 scopus 로고    scopus 로고
    • Relatively robust representations of symmetric tridiagonals
    • B. N. PARLETT AND I. S. DHILLON, Relatively robust representations of symmetric tridiagonals, Linear Algebra Appl., 309(2000), pp. 121-151.
    • (2000) Linear Algebra Appl. , vol.309 , pp. 121-151
    • Parlett, B.N.1    Dhillon, I.S.2
  • 31
    • 0034379502 scopus 로고    scopus 로고
    • An implementation of the dqds algorithm (positive case)
    • B. N. PARLETT AND O. A. MARQUES, An implementation of the dqds algorithm (positive case), Linear Algebra Appl., 309(2000), pp. 217-259.
    • (2000) Linear Algebra Appl. , vol.309 , pp. 217-259
    • Parlett, B.N.1    Marques, O.A.2
  • 34
  • 35
    • 84856544343 scopus 로고    scopus 로고
    • Detecting localization in an invariant subspace
    • C. VÖMEL AND B. N. PARLETT, Detecting localization in an invariant subspace, SIAM J. Sci. Comput. 33(2011), pp. 3447-3467.
    • (2011) SIAM J. Sci. Comput , vol.33 , pp. 3447-3467
    • Vömel, C.1    Parlett, B.N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.