系統識別號 U0026-2708201616463100 論文名稱(中文) 小樣本統計條件數估計估算數值代數問題 論文名稱(英文) Small-Sample Statistical Condition Number Estimations for Numerical Algebra Problems 校院名稱 成功大學 系所名稱(中) 數學系應用數學碩博士班 系所名稱(英) Department of Mathematics 學年度 104 學期 2 出版年 105 研究生(中文) 蔡尚亨 研究生(英文) Shang-Heng Tsai 學號 l16021153 學位類別 碩士 語文別 英文 論文頁數 32頁 口試委員 指導教授-王辰樹口試委員-陳旻宏口試委員-黃聰明口試委員-黃印良 中文關鍵字 條件數  線性系統  特徵值  狀態迴溯極點配置 英文關鍵字 condition number  linear system  eigenvalue  state feedback pole assignment 學科別分類 中文摘要 在這篇碩士論文中，我們研究小樣本統計條件數估計估算不同的數值代數問題的條件數。SSCE是在機率的觀點之下估計數值問題的條件數，主要是目標問題對於微分部分的估計。在這篇碩士論文中，我們計畫用SSCE分別去算線性系統、特徵值問題、狀態迴溯極點配置問題。 英文摘要 In this thesis, we study small sample statistical condition number estimation (SSCE) to estimate the condition numbers of various numerical algebra problems. Method SSCE is used to estimate the condition number of a numerical problem in a probability sense. The main task of SSCE involves estimating the derivative part of the target problem. In this thesis, we plan to use SSCE on linear systems, eigenvalue problems, and state feedback pole assignment problems, to estimate individual condition numbers, respectively. 論文目次 1 Introduction 1 2 A Brief Survey of Small- Sample Statistical Condition Estimation(SSCE) 3 3 Condition Number of a Linear System 6 3.1 Condition number of matrix-vector multiplication with f(x) = Ax . . . 6 3.2 Condition number of linear system with f(x) = A^(-1)x .......... 9 4 Condition Number of an Eigenvalue Problem 12 5 State Feedback Pole Assignment Problem 18 6 Conclusion 30 參考文獻 [1] C.S. Kenney and A.J. Laub, Small-sample statistical condition estimates for general matrix functions, SIAM J. Sci. Comput (1994), Vol. 15(1), pp. 36-61. [2] T. Gudmundsson, C.S. Kenney and A.J. Laub, Small- sample statistical estimates for the sensitivity of eigenvalue problems, SIAM. J. Matrix Anal., Appl., (1997), Vol. 18(4), pp. 868-886. [3] E.K. Chu, C.-S. Wang, C.-Y. Weng and C.-C. Yen, Conditioning of state feedback pole assignment problems, TJM, (2012), Vol. 16(1), pp. 283-304. [4] V. Mehrmann and H. Xu, An analysis of the pole placement problem. I. The single-input case, ETNA, (1996), vol. 4, pp. 89-105. [5] J.G. Sun, Perturbation analysis of the pole assignment problem, SIAM J. Matix Anal. Appl. (1996), vol. 17, pp. 313-331. [6] Ching-Chang Yen, Perturbation analysis related to linear dynamical control problems, PhD Thesis, Oct. 2011. [7] Lloyd N. Trefethen, David Bau III. Numerical linear algebra, Cambridge University Press, 1997. [8] N. J. Higham, Accuracy and stability of numerical algorithms, 2nd ed., SIAM, Philadelphia, PA, 2002. [9] W. Wang, C.-S. Wang, Y. Wei and P. Xie, Mixed, componentwise condition numbers and small sample statistical condition estimation for generalized spectral projections and matrix sign functions, TJM, 2016, Vol. 20(2), pp. 333-363. 論文全文使用權限 同意授權校內瀏覽/列印電子全文服務，於2017-01-13起公開。同意授權校外瀏覽/列印電子全文服務，於2017-01-13起公開。

 如您有疑問，請聯絡圖書館 聯絡電話：(06)2757575#65773 聯絡E-mail：etds@email.ncku.edu.tw