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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.
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