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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/36393
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dc.contributor.advisor王太林zh_TW
dc.contributor.advisorWang, Tai-Linen_US
dc.contributor.author張天財zh_TW
dc.contributor.authorChang, Tian-Tsairen_US
dc.creator張天財zh_TW
dc.creatorChang, Tian-Tsairen_US
dc.date1998en_US
dc.date.accessioned2009-09-18T10:28:12Z-
dc.date.available2009-09-18T10:28:12Z-
dc.date.issued2009-09-18T10:28:12Z-
dc.identifierB2002001691en_US
dc.identifier.urihttps://nccur.lib.nccu.edu.tw/handle/140.119/36393-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用數學研究所zh_TW
dc.description85751005zh_TW
dc.description87zh_TW
dc.description.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。zh_TW
dc.description.abstractIn 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.en_US
dc.description.tableofcontents1.Introduction.........................................................................................1\r\n1.1 Lanczos Process...............................................................................1\r\n1.2 Orthogonal Polynomials..................................................................4\r\n1.3 Lanczos-type Methods.....................................................................6\r\n1.4 DG Method......................................................................................10\r\n1.5 HH Method......................................................................................12\r\n1.6 TQR Methods..................................................................................14\r\n2. Examples and Numerical Results...................................................... 16\r\n 2.1 Examples......................................................................................16\r\n2.2 Comparison of the Algorithms ........................................................17\r\n3. Conclusion..........................................................................................20\r\n Bibliography..........................................................................................21\r\n Appendix................................................................................................22zh_TW
dc.language.isoen_US-
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#B2002001691en_US
dc.subject賈可比矩陣zh_TW
dc.subject蘭可修斯過程zh_TW
dc.subjectJacobi matrixen_US
dc.subjectLanczos processen_US
dc.title有關賈可比矩陣數值建構上的討論zh_TW
dc.titleOn the Numerical Construction of a Jacobi Matrixen_US
dc.typethesisen
dc.relation.reference[1] G. S. Ammar and Chunyang He, On an inverse eigenvalue problem for unitary Hessenberg matrices, Linear Algebra Appl. 218 (1995), 263-271.zh_TW
dc.relation.reference[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.zh_TW
dc.relation.reference[3] D. Boley and G. H. Golub, A survey of matrix inverse eigenvalue problems, Inverse Problems 3 (1987), 595-622.zh_TW
dc.relation.reference[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.zh_TW
dc.relation.reference[5] M. T. Chu, Inverse eigenvalue problems, SIAM. Rev. 40 (1998), 1-39.zh_TW
dc.relation.reference[6] B. N. Datta, Numerical Linear Algebra and Applications, Brooks/Cole, Pacific Grove, California, 1995.zh_TW
dc.relation.reference[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.zh_TW
dc.relation.reference[8] W. Gautschi, Computational aspects of orthogonal polynomials, P.Nevai(ed.), 181-216, 1990 Kluwer Academin Publishers.zh_TW
dc.relation.reference[9] W. B. Gragg, The QR algorithm for unitary Hessenberg matrices, J. Comput. Appl. Math. 16 (1968), 1-8.zh_TW
dc.relation.reference[10] L. J. Gray and D. G .Wilson, Construction of a Jacobi matrix from spectral data, Linear Algebra Appl.14 (1976),131-134.zh_TW
dc.relation.reference[11] H. Hochstadt, On the construction of a Jacobi matrix from spectral data, Linear Algebra Appl. 8 (1974), 435-446.zh_TW
dc.relation.reference[12] H. Hochstadt, On some inverse problems in matrix theory, Ariciv der Math. 18 (1967), 201-207.zh_TW
dc.relation.reference[13] T. Y. LI, and Zhonggang Zeng, The Laguerre iteration in solving the symmetric tridiagonal eigenproblem, revisted, SIAM. J. Comput. 15 (1994), 1145-1173.zh_TW
dc.relation.reference[14] B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice Hall, Englewood Cliffs, N. J. 1980.zh_TW
dc.relation.reference[15] L. Reichel, Fast QR decomposition of Vandermonde-like matrices and polynomial least squares approximation, SIAM J. Matrix Anal. Appl. 12 (1991), 552-564.zh_TW
dc.relation.reference[16] T-L. Wang, Notes on some basic matrix eigenproblem computations, unpublished manuscript.zh_TW
item.languageiso639-1en_US-
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item.grantfulltextopen-
item.openairetypethesis-
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