Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Matrix theory

Some Research about the Property of Refined Approximate Eigenvector Problems

Author LiuJunWei
Tutor ChenGuiZhi
School Xiamen University
Course Computational Mathematics
Keywords Eigenvalue problem Arnoldi method Refined Arnoldi method Refined Ritz vectors
CLC O151.21
Type Master's thesis
Year 2009
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This paper studies the fine approximation of the nature of the feature vectors , including solving symmetric eigenvalue problem between the refined vector orthogonal refined Arnoldi method and how to solve the matrix multiple eigenvalues ??. The text is divided into three chapters . The first chapter describes the source of the problem of large-scale matrix , the basic method to solve this kind of problem and the development of the discipline dynamic , and outlines the main work of this paper . The second chapter studies the refined Ritz vector orthogonal . In finite precision , how refined Arnoldi method seeking a set of orthogonal symmetric matrix extent can reach the the machine precision approximate eigenvectors group of . This chapter first gives a new expression of the refined Ritz vectors , the expression that theoretically different characteristics approximate value , generally can not be guaranteed refined Arnoldi method to determine the refined Ritz vector orthogonal group . Further mining orthogonal method can get a set of orthogonal degree of machine precision can reach the standard orthogonal approximate eigenvectors group . Finally , the numerical results to verify the accuracy of the conclusions obtained after orthogonal approximation of the amount of residue is unchanged . The third chapter studies how refined Arnoldi method gives the eigenvalues ??approximation and estimate its multiplicity . This chapter first study refined approximation eigenvectors of nature , the nature that refined Arnoldi method can not be determined directly repeated characteristic roots of multiplicity . Further , the chapter presents a refined Arnoldi method to determine the multiplicity of the eigenvalue algorithm, numerical case shows the feasibility of the algorithm .

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