Convergence Analysis of Inexact Rayleigh Quotient Iteration

2003 ◽  
Vol 24 (3) ◽  
pp. 627-644 ◽  
Author(s):  
Yvan Notay
Keyword(s):  
Convergence Analysis ◽  
Rayleigh Quotient ◽  
Rayleigh Quotient Iteration

scholarly journals A Study on the Convergence Analysis of the Inexact Simplified Jacobi–Davidson Method

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jutao Zhao ◽  
Pengfei Guo
Keyword(s):  
Convergence Analysis ◽  
Iteration Method ◽  
Eigenvalue Problems ◽  
Rayleigh Quotient ◽  
Convergence Factor ◽  
Cubic Convergence ◽  
Davidson Method ◽  
Outer Iteration ◽  
Rayleigh Quotient Iteration ◽  
Inner Iteration

The Jacobi–Davidson iteration method is very efficient in solving Hermitian eigenvalue problems. If the correction equation involved in the Jacobi–Davidson iteration is solved accurately, the simplified Jacobi–Davidson iteration is equivalent to the Rayleigh quotient iteration which achieves cubic convergence rate locally. When the involved linear system is solved by an iteration method, these two methods are also equivalent. In this paper, we present the convergence analysis of the simplified Jacobi–Davidson method and present the estimate of iteration numbers of the inner correction equation. Furthermore, based on the convergence factor, we can see how the accuracy of the inner iteration controls the outer iteration.

Quantum algorithm for Laplacian eigenmap via Rayleigh quotient iteration

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Ze-Tong Li ◽  
Fan-Xu Meng ◽  
Xu-Tao Yu ◽  
Zai-Chen Zhang
Keyword(s):  
Quantum Algorithm ◽  
Rayleigh Quotient ◽  
Rayleigh Quotient Iteration

scholarly journals Multigrid Discretization and Iterative Algorithm for Mixed Variational Formulation of the Eigenvalue Problem of Electric Field

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Yidu Yang ◽  
Yu Zhang ◽  
Hai Bi
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Electric Field ◽  
Adaptive Algorithm ◽  
Variational Formulation ◽  
High Efficiency ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Rayleigh Quotient ◽  
Rayleigh Quotient Iteration

This paper discusses highly finite element algorithms for the eigenvalue problem of electric field. Combining the mixed finite element method with the Rayleigh quotient iteration method, a new multi-grid discretization scheme and an adaptive algorithm are proposed and applied to the eigenvalue problem of electric field. Theoretical analysis and numerical results show that the computational schemes established in the paper have high efficiency.

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