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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/85496
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dc.contributor.advisor王太林zh_TW
dc.contributor.author賴信憲zh_TW
dc.creator賴信憲zh_TW
dc.date2000en_US
dc.date.accessioned2016-04-18T08:31:43Z-
dc.date.available2016-04-18T08:31:43Z-
dc.date.issued2016-04-18T08:31:43Z-
dc.identifierA2002001738en_US
dc.identifier.urihttp://nccur.lib.nccu.edu.tw/handle/140.119/85496-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用數學系zh_TW
dc.description86751004zh_TW
dc.description.abstract我們將原本求只有實根的多項式問題轉換為利用QR方法求一個友矩陣(companion matrix)或是對稱三對角(symmetric tridiagonal matrix)的特徵值問題，在數值測試中顯示出利用傳統演算法去求多項式的根會比求轉換過後矩陣特徵值的方法較沒效率。zh_TW
dc.description.abstractGiven a polynomial pn(x) of degree n with real roots, we transform the problem of finding all roots of pn (x) into a problem of finding the eigenvalues of a companion matrix or of a symmetric tridiagonal matrix, which can be done with the QR algorithm. Numerical testing shows that finding the roots of a polynomial by standard algorithms is less efficient than by computing the eigenvalues of a related matrix.en_US
dc.description.tableofcontents封面頁\r\n證明書\r\n致謝詞\r\n論文摘要\r\n目錄\r\n1. Introduction\r\n2. Basic Principles\r\n2.1 Conditioning of a Problem\r\n2.2 Computing the Eigenvalues of a Matrix\r\n3. Numerical Methods\r\n3.1 LG Method, JT Method and JTC Method\r\n3.2 C-HQR Method\r\n3.3 E-TQR Method\r\n4. Numerical Examples and Results\r\n4.1 Examples\r\n4.2 Comparision of the Algorithms\r\n5. Conclusions\r\nReferences\r\nAppendix\r\nAppendix A: Orthogonal Polynomials\r\nAppendix B: Programszh_TW
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#A2002001738en_US
dc.subject傳統解多項式的方法zh_TW
dc.subject三對角矩陣zh_TW
dc.subjectQR演算法zh_TW
dc.subjectpolynomial root-findingen_US
dc.subjectsymmetric tridiagonal matrixen_US
dc.subjectQR algorithmen_US
dc.title利用計算矩陣特徵值的方法求多項式的根zh_TW
dc.titleFinding the Roots of a Polynomial by Computing the Eigenvalues of a Related Matrixen_US
dc.typethesisen_US
dc.relation.reference[1] I. Bar-On and B. Codenotti, A fast and stable parallel QRalgorithm for symmetric tridiagonal matrices, Linear Algebra Appl. 220 (1995), 63-95.\r\n[2] L. Brugnano and D. Trigiante, Polynomial Roots: The Ultimate Answer?, Linear Algebra Appl. 225 (1995), 207-219.\r\n[3] B. N. Datta, Numerical Linear Algebra and Applications, Brooks/Cole, Pacific Grove, California, 1995.\r\n[4] Edelman and H. Murakami, Polynomial roots from companion matrix eigenvalues, Math. Comp. 64 (1995), 763-776.\r\n[5] S. Goedecker, Remark on algorithms to find roots of polynomials, SIAM J. Sci. Comput. 15 (1994), 1059-1063.\r\n[6] IMSL User s manual, version 1.0 (1997), chapter 7.\r\n[7] C. Moler, Cleve s corner: ROOTS-of polynomials, The Mathworks Newsletter. 5 (1991), 8-9.\r\n[8] B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, N. J. 1980.\r\n[9] V. Pan, Solving a polynomial equation: Some history and recent progress, SIAM Rev. 39 (1997), 187-220.\r\n[10] G. Schmeisser, A real symmetric tridiagonal matrix with a given characteristic polynomial, Linear Algebra Appl. 193 (1993), 11-18.\r\n[11] N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, Philadelphia, 1997.zh_TW
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