Optimal algorithms in a Krylov subspace for iteratively solving the Rayleigh quotient as the eigenvalue of a symmetric matrix
Date Issued
2014
Date
2014
Author(s)
Lin, Jin-Yen
Abstract
Eigenvalue problem is a very common problem in engineering and mathematics, there are many other forms of problem converted from eigenvalue problem, and how to efficiently and accurately solve the eigenvalue problem is a very important topic for engineerning.
This study wants to present Krylov subspace methods and Rayleigh quotient concept and with the Arnoldi process to extend the new iterative method to solve the matrix eigenvalue problem, however iterative process more than one way, this study will compare and select the best method applied in various types of matrix, and mode shapes modulus of large structures in civil engineering can also use this method to explore the efficiency of new method.
The method of this study can calculated eigenvales where matlab can not run out of inlarge symmetric matrices.
Finally, this method can only be used in a symmetric matrix symmetric matrix, the reason will be mentioned in the final conclusion.
This study wants to present Krylov subspace methods and Rayleigh quotient concept and with the Arnoldi process to extend the new iterative method to solve the matrix eigenvalue problem, however iterative process more than one way, this study will compare and select the best method applied in various types of matrix, and mode shapes modulus of large structures in civil engineering can also use this method to explore the efficiency of new method.
The method of this study can calculated eigenvales where matlab can not run out of inlarge symmetric matrices.
Finally, this method can only be used in a symmetric matrix symmetric matrix, the reason will be mentioned in the final conclusion.
Subjects
特徵值
Krylov 子空間法
Rayleigh quotient(雷利商數)
Arnoldi化過程
振態模數
Type
thesis
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