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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/89759


    Title: QR與LR算則之位移策略
    On the shift strategies for the QR and LR algorithms
    Authors: 黃義哲
    HUANG, YI-ZHE
    Contributors: 王太林
    WANG, TAI-LIN
    黃義哲
    HUANG, YI-ZHE
    Keywords: 位移策略
    特徵向量
    特徵值
    QR algorithm, LR algorithm, modified Cholesky algorithm.
    Date: 1992
    1991
    Issue Date: 2016-05-02 17:07:19 (UTC+8)
    Abstract: 用QR與LR迭代法求矩陣特徵值與特徵向量之過程中，前人曾提出位移策略以加速其收斂速度，其中最有效的是Wilkinson 移位值。在此我們希望尋求能使收斂更快速的位移值。
    Abstract
    Reference: References:
    [l] Dekker, T . J. and Traub, J. F., 1971. "The Shifted QR Algorithm for Hermitian
    Matrices." Linear Algebra and Its Applications, 4:137-154
    [2] Dubrulle, A., 1970. "A Short Note on the Implicit QL Algorithm for Symmetric
    Tridiagonal Matrix." Numer. Math. , 15 :450.
    [3] Golub, G. H. and Van Loan, C. F. , 1989. Matrix Computations. 2nd edition,
    Baltimore, MD: The Johns Hopkins University Press.
    [4] Jiang, E. and Zheng, Z., 1985. "A New Shift of the QL Algorithm for Irreducible
    Symmetric Tridiagonal Matrices." Linear Algebra and Its Applications,65:261-272.
    [5] Ortega, J. M. and Kaiser, H. F., 1963. "The LLT and QR Methods for Symmetric
    Tridiagonal matrices." Computer Journal, 99-101.
    [6] Parlett, B. N. , 1964. "The Development and Use of Methods of LR Type."
    SIAM Review, 6:275-295 .
    [7] Parlett, B. N., 1966. "Singular and Invariant Matrices Under the QR Transformation. " Math. Comp., 611-615.
    [8] Parlett, B. N., 1980. The Semmetric Eigenvalue Problem. Prentice-Hall Inc. ,
    Englewood Cliffs 1980.
    [9] Rutishauser, H. and Schwarz, H. R., 1963. "The LR Transformation Method
    for Symmetric Matrices." Numer. Math. 5:273-289.
    [10] Saad, Y. , 1974, "Shift of Origin for the QR Algorithm." Toronto: Proceedings
    IFIP Congress.
    [11] Smith, B. T. and Boyle, J. M., 1974. Matrix Eigensystem Routines - EISPACK
    Guide, Springer Verlag.
    [12] `Ward, R. C. and Gray, L. J ., 1978. "Eigensystem Computation for Skew-Symmetric Matrices and a Class of Symmetric Matrices." A CM Trans. on
    Math. Software , 4:278-285 .
    [13] Wilkinson, J. H. and Reisch, C., 1961. Handbook for A`l?tomatric Computation.
    Volum. II. Linear Algebra, Springer Verlag.
    [14] Wilkinson, J. H. , 1968. "Global Convergence of Tridiagonal QR Algorithm
    with Origin Shifts." Linear Algebra and Its Applications, 1:409-420.
    Notation Convention:
    (1) CHOLESKY: This subroutine is the implementation of the modified LLT
    algorithm.
    (2)imTQLl: This subroutine from the EISPACK computes the eigenvalues.
    by the implicit QL algorithm.
    (3) imTQL2: This subroutine from the EISPACK computes the eigenvalues
    and eigenvectors at the same tims by the implicit QL method.
    (4) imTQL2s4l: This routine first computes eigenvalues by CHOLESKY and
    then uses these eigenvalues as shifts in imTQL2.
    (5) imTQL2s42: This subroutine makes the use of imTQL1 to compute the
    eigenvalues and then uses these computed values as shifts in imTQL2 . .
    (6) TQL1: This subroutine from the EISPACK computes eigenvalues by the
    QL method.
    (7) TQL1s31, TQL1s32, TQL1s33 : These subroutines are the test of the use
    of 83 , described in section 3.
    (8) TQL2: This subroutine from the EISPACK computes eigenvalues and
    eigenvectors simultaneously by the QL method.
    (9) TQL2s41: This subroutine calculate eigenvalues by CHOLESKY at first
    and then uses these eigenvalues as shifts in TQL2.
    (1 0) TQL2s42: This subroutine uses eigenvalues computed by TQL1 as shifts
    in TQL2.
    Description: 碩士
    國立政治大學
    應用數學系
    Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002004735
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

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