政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/85496

English | 正體中文 | 简体中文 | Post-Print筆數 : 27 | Items with full text/Total items : 114205/145239 (79%)
Visitors : 52921568 Online Users : 935

RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.

Scope

please add "double quotation mark" for query phrases to get precise results

please goto advance search for comprehansive author search

Adv. Search

Home ‧ Login ‧ Upload ‧ Help ‧ About ‧ Administer

Goto mobile version

政大機構典藏 > 理學院 > 應用數學系 > 學位論文 > Item 140.119/85496

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/85496

Title:	利用計算矩陣特徵值的方法求多項式的根 Finding the Roots of a Polynomial by Computing the Eigenvalues of a Related Matrix
Authors:	賴信憲
Contributors:	王太林賴信憲
Keywords:	傳統解多項式的方法三對角矩陣 QR演算法 polynomial root-finding symmetric tridiagonal matrix QR algorithm
Date:	2000
Issue Date:	2016-04-18 16:31:43 (UTC+8)
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。 Given 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.
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. [2] L. Brugnano and D. Trigiante, Polynomial Roots: The Ultimate Answer?, Linear Algebra Appl. 225 (1995), 207-219. [3] B. N. Datta, Numerical Linear Algebra and Applications, Brooks/Cole, Pacific Grove, California, 1995. [4] Edelman and H. Murakami, Polynomial roots from companion matrix eigenvalues, Math. Comp. 64 (1995), 763-776. [5] S. Goedecker, Remark on algorithms to find roots of polynomials, SIAM J. Sci. Comput. 15 (1994), 1059-1063. [6] IMSL User s manual, version 1.0 (1997), chapter 7. [7] C. Moler, Cleve s corner: ROOTS-of polynomials, The Mathworks Newsletter. 5 (1991), 8-9. [8] B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, N. J. 1980. [9] V. Pan, Solving a polynomial equation: Some history and recent progress, SIAM Rev. 39 (1997), 187-220. [10] G. Schmeisser, A real symmetric tridiagonal matrix with a given characteristic polynomial, Linear Algebra Appl. 193 (1993), 11-18. [11] N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, Philadelphia, 1997.
Description:	碩士國立政治大學應用數學系 86751004
Source URI:	http://thesis.lib.nccu.edu.tw/record/#A2002001738
Data Type:	thesis
Appears in Collections:	[應用數學系] 學位論文

Files in This Item:

File	Size	Format
index.html	0Kb	HTML2	306	View/Open

All items in 政大典藏 are protected by copyright, with all rights reserved.

社群 sharing

著作權政策宣告 Copyright Announcement

1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.

DSpace Software Copyright © 2002-2004 MIT & Hewlett-Packard / Enhanced by NTU Library IR team Copyright © - Feedback