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Refined Jacobi-Davidson Type Method for a Right Definite Two-Parameter Eigenvalue Problem

Author: ZuoZhongMing
Tutor: LuLinZuo
School: Xiamen University
Course: Computational Mathematics
Keywords: Right fixed between two parameter eigenvalue problem Jacobi-Davidson method Correcting equation Ritz on Refined Ritz pairs Refined Jacobi-Davidson method
CLC: O241.6
Type: Master's thesis
Year: 2009
Downloads: 10
Quote: 0
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Abstract


This article discusses the following form so-called two-parameter eigenvalue problem : A 1 x 1 = λB 1 x 1 μC 1 x 1 , A 2 x 2 = λB 2 x 2 μC 2 x 2 . here's a i , B i , C i is n i × n i matrix , x i is n i -dimensional vector , i = 1,2. if (λ, μ), x 1 , x 2 satisfies the above equation , then the function (λ, μ) for the eigenvalues ??, tensor plot x 1 (?) x 2 is called eigenvectors two parameter eigenvalue problem has a wide range of applications . literature is proposed to solve the above problem right feature set two parameters value problem for Jacobi-Davidson type methods in the literature , the authors MEHochstenbach and B.Plestenjak that refinement method is not suitable for two-parameter eigenvalue problem, and that two-parameter eigenvalue problem solving refinement method , there are three problems : the refined Ritz vectors poor convergence , computing capacity, can not calculate multiple eigenvalues ??paper that is not true. Given two arguments against the right eigenvalue problem , this paper proposes an efficient numerical method for refinement . Proved by theoretical and numerical experiments illustrate the convergence of Ritz values ??and Ritz vectors have refined than the usual Ritz vectors better convergence text is divided into five parts: The first chapter briefly describes the two parameter eigenvalue problem and its context ; second chapter describes the solution proposed in the literature the right set two parameters eigenvalue problems Jacobi-Davidson type methods ; Chapter proved Ritz value convergence ( Theorem 4 ) , and through this description of the essence of the Ritz vectors has better convergence , citing specific examples to illustrate this ; proposed in Chapter proposed algorithm ; first five chapters of numerical experiments verify the superiority of our algorithm and give conclusions.

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