政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/36393
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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/36393


    Title: 有關賈可比矩陣數值建構上的討論
    On the Numerical Construction of a Jacobi Matrix
    Authors: 張天財
    Chang, Tian-Tsair
    Contributors: 王太林
    Wang, Tai-Lin
    張天財
    Chang, Tian-Tsair
    Keywords: 賈可比矩陣
    蘭可修斯過程
    Jacobi matrix
    Lanczos process
    Date: 1998
    Issue Date: 2009-09-18 18:28:12 (UTC+8)
    Abstract: 這篇論文使用前人所提出的七種方法LMGS、ITQR、imITQR、CB、HH、TLD和TLS，去造一個賈可比(Jacobi)矩陣。文中我們使用已知的特徵值(eigenvalue)和特徵向量的第一個成份，去運作這些演算法，並列出數值的結果，以比較這六種方法造出來的賈可比矩陣之準確性。
    In this thesis seven methods LMGS、ITQR、imITQR、CB、HH、TLS and TLD developed in the past are applied to construct a Jacobi matrix. We use the known eige-envalues and the first components of eigenvctors of a Jacobi matrix to execute thes-e algorithms and list the numerical results and compare the accuracy of the computed Jacobi matrix.
    Reference: [1] G. S. Ammar and Chunyang He, On an inverse eigenvalue problem for unitary Hessenberg matrices, Linear Algebra Appl. 218 (1995), 263-271.
    [2] G. S. Ammar and W. Gragg and L. Reichel, Constructing a unitary Hessenberg matrix from spectral data, in G. H. Golub and P. Van Dooren, Eds., Numerical. Linear. Algebra, Digital Signal Processing and Parallel Algorithms (Springer, N Y, 1991) 358-396.
    [3] D. Boley and G. H. Golub, A survey of matrix inverse eigenvalue problems, Inverse Problems 3 (1987), 595-622.
    [4] C. de Boor and G. H. Golub, The numerically stable reconstruction of a Jacobi matrix from spectral data, Linear Algebra Appl. 21 (1978), 245-260.
    [5] M. T. Chu, Inverse eigenvalue problems, SIAM. Rev. 40 (1998), 1-39.
    [6] B. N. Datta, Numerical Linear Algebra and Applications, Brooks/Cole, Pacific Grove, California, 1995.
    [7] S. Elhay, G. H. Golub, and J. Kautsky, Updating and downdating of orthogonal polynomials with data fitting applications, SIAM J. Matrix Anal. 12 (1991), 327-353.
    [8] W. Gautschi, Computational aspects of orthogonal polynomials, P.Nevai(ed.), 181-216, 1990 Kluwer Academin Publishers.
    [9] W. B. Gragg, The QR algorithm for unitary Hessenberg matrices, J. Comput. Appl. Math. 16 (1968), 1-8.
    [10] L. J. Gray and D. G .Wilson, Construction of a Jacobi matrix from spectral data, Linear Algebra Appl.14 (1976),131-134.
    [11] H. Hochstadt, On the construction of a Jacobi matrix from spectral data, Linear Algebra Appl. 8 (1974), 435-446.
    [12] H. Hochstadt, On some inverse problems in matrix theory, Ariciv der Math. 18 (1967), 201-207.
    [13] T. Y. LI, and Zhonggang Zeng, The Laguerre iteration in solving the symmetric tridiagonal eigenproblem, revisted, SIAM. J. Comput. 15 (1994), 1145-1173.
    [14] B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice Hall, Englewood Cliffs, N. J. 1980.
    [15] L. Reichel, Fast QR decomposition of Vandermonde-like matrices and polynomial least squares approximation, SIAM J. Matrix Anal. Appl. 12 (1991), 552-564.
    [16] T-L. Wang, Notes on some basic matrix eigenproblem computations, unpublished manuscript.
    Description: 碩士
    國立政治大學
    應用數學研究所
    85751005
    87
    Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002001691
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

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