Superconvergence two-grid scheme based on shifted-inverse power method for eigenvalue problems by function value recovery

2017 ◽  
Vol 320 ◽  
pp. 218-236
Author(s):  
Huipo Liu ◽  
Shuanghu Wang ◽  
Huayun Shen
Keyword(s):  
Eigenvalue Problems ◽  
Inverse Power ◽  
Power Method ◽  
Value Recovery ◽  
Grid Scheme

A Nonlinear Inverse Power Method with Shift

1983 ◽  
Vol 20 (6) ◽  
pp. 1147-1152 ◽  
Author(s):  
Jean Descloux ◽  
Jacques Rappaz
Keyword(s):  
Inverse Power ◽  
Power Method

A Two-Grid Method of Nonconforming Element Based on the Shifted-Inverse Power Method for the Steklov Eigenvalue Problem

2013 ◽  
Vol 694-697 ◽  
pp. 2918-2921
Author(s):  
Hai Bi
Keyword(s):  
Eigenvalue Problem ◽  
High Efficiency ◽  
Grid Method ◽  
Inverse Power ◽  
Power Method ◽  
Discretization Scheme ◽  
Nonconforming Element ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem ◽  
Numer Anal

This paper establishes a new kind of two-grid discretization scheme of nonconforming Crouzeix-Raviart element based on the shifted-inverse power method for the Steklov eigenvalue problem. The error estimates are provided from the work of Yang and Bi (SIAM J. Numer. Anal., 49, pp.1602-1624, 2011). Finally, numerical experiments are reported to illustrate the high efficiency of the two-grid discretization scheme proposed in this paper.

scholarly journals A multigrid method for eigenvalue problems based on shifted-inverse power technique

2015 ◽  
Vol 1 (1) ◽  
pp. 207-228 ◽  
Author(s):  
Hongtao Chen ◽  
Yunhui He ◽  
Yu Li ◽  
Hehu Xie
Keyword(s):  
Multigrid Method ◽  
Eigenvalue Problems ◽  
Inverse Power

scholarly journals Study on Eigen Values and Eigen Vectors of Matrices : An Iterative Approach

2018 ◽  
Vol 37 ◽  
pp. 51-61
Author(s):  
ARM Jalal Uddin Jamali ◽  
Md Hasibul Haque ◽  
Md Sah Alam
Keyword(s):  
Iterative Algorithm ◽  
The Other ◽  
Negative Sign ◽  
Inverse Power ◽  
Iterative Approach ◽  
Power Method ◽  
Other Hand ◽  
Eigen Values

Power method is frequently used for finding largest Eigen-pair. On the other hand, Inverse Power method is utilized to find smallest Eigen-pair. Using shifting property, Power method and/or Inverse Power method can be used to find out other desired Eigen pairs too. Several lemmas based on Power method with shifting property are presented here. Moreover, a Modified Hybrid Iterative Algorithm based upon both Power method and Inverse Power method is proposed to find both largest and smallest Eigen-pairs simultaneously with ease. Several experiments have been performed to investigate the robustness and effectiveness of the algorithm. The proposed algorithm is able to find both (largest and smallest) Eigen-pairs successfully and efficiently. Moreover, the proposed algorithm is able to find out the nature (positive and negative sign) of the Eigen values and in some cases the algorithm is also able to find out the second largest Eigen pair in consequence.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 51-61

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