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研究生:黃俊豪
研究生(外文):Chun-Hao Huang
論文名稱:三次特徵多項式的子空間逼近法
論文名稱(外文):A Subspace Approximation Method For The Cubic Eigenvalue Problem
指導教授:黃榮秋黃榮秋引用關係
指導教授(外文):Grorge R. Hwang
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:33
中文關鍵詞:Eigenvalue
外文關鍵詞:特徵值
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三次特徵多項式在Krylov子空間上的逼近法.
This paper introduces a method that uses perturbation subspaces for block eigenvector matrices to reduce the modified problem to a sequence of problems of smaller-dimention . These perturbation subspaces are shown to be contained in certain generalized Krylov subspaces of the n-dimentional space , where n is the unbounded dimention of the matrices in the cubic problem . The method converges at least as fast as the corresponding Taylor series , and the convergence can be accelerated further by applying a block generalization of the cubic convergent Rayleigh quptient iteration . Numerical examples are presented to illustrate the applicability of the method .
[1] L.V.Ahlfors, Complex Analysis, McGraw-Hill Book Company, third ed.,1979.
[2] T.Kato, Perturbation Theory for Linear Operators, Spinger-Verlag,1980.
[3] Weichung Wang,Tsung-Min Hwang,Wen-Wei Lin,Jinn-Liang Lin, Numerical methods for semiconductor heterostructures with band nonparabolicity, Journal of Computational Physics 190(2003) 141-158.
[4] U.B.Holz,Subspace Approximation Methods for Perturbed Quadratic Eigenvalue Problems, PhD thesis, Mathematics Department, Stanford University, 2002
[5] F.S.Acton, numerical methods That Work (Harper and Rrow , New York , 1970) , pp477-498
[6] D.A.Faster,The Physics of Semiconductor Devices , ed . (Oxford , London , 1979 )
[7] Ben Noble , James W. Daniel , Applied Linear Algebra , ed . (Prentice-Hall,NewJersy,1988)
[8] Biswa Nath Datta , Numerical Linar Algebra and Apllications(Brooks/Coke,1975).
[9] G.L.Snider, I.-H. Tan, and E.L.Hu,”Electron states in mesaetched one-dimensinal quantum well wires,” J.Appl,Phys.68(6),pp.2849-2853,September 1990
[10] Richard L. Burden , J. Douglas Faires , Numerical Analysis.
[11] Mathematical Analysis , A Modern Approach to Advanced Calculus .
(Tom M. Apostol , 1957)
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