Rayleigh Quotient Iteration, an old recipe for solving modern large-scale eigenvalue problems

1998 ◽  
Vol 12 (1) ◽  
pp. 22 ◽  
Author(s):  
J. Descloux ◽  
J.-L. Fattebert ◽  
F. Gygi ◽  
Ralf Gruber ◽  
Jacques Rappaz
Keyword(s):  
Large Scale ◽  
Eigenvalue Problems ◽  
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
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