A new Monte Carlo power method for the eigenvalue problem of transfer matrices

1993 ◽  
Vol 71 (1-2) ◽  
pp. 269-297 ◽  
Author(s):  
Tohru Koma
Keyword(s):  
Monte Carlo ◽  
Eigenvalue Problem ◽  
Power Method ◽  
Transfer Matrices

Practical Monte Carlo simulation using modified power method with preconditioning

2019 ◽  
Vol 127 ◽  
pp. 372-384 ◽  
Author(s):  
Peng Zhang ◽  
Hyunsuk Lee ◽  
Matthieu Lemaire ◽  
Chidong Kong ◽  
Jiwon Choe ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Power Method

On the power method for quaternion right eigenvalue problem

2019 ◽  
Vol 345 ◽  
pp. 59-69 ◽  
Author(s):  
Ying Li ◽  
Musheng Wei ◽  
Fengxia Zhang ◽  
Jianli Zhao
Keyword(s):  
Eigenvalue Problem ◽  
Power Method

The Modified Power Method for Solving the Eigenvalue Problem with the Use of Idempotent Matrix

2015 ◽  
Vol 712 ◽  
pp. 43-48
Author(s):  
Rafał Palej ◽  
Artur Krowiak ◽  
Renata Filipowska
Keyword(s):  
Eigenvalue Problem ◽  
Rate Of Convergence ◽  
Rayleigh Quotient ◽  
Frobenius Norm ◽  
Dominant Eigenvalue ◽  
Power Method ◽  
New Approach ◽  
Idempotent Matrix ◽  
The Given ◽  
Scaling Coefficient

The work presents a new approach to the power method serving the purpose of solving the eigenvalue problem of a matrix. Instead of calculating the eigenvector corresponding to the dominant eigenvalue from the formula , the idempotent matrix B associated with the given matrix A is calculated from the formula , where m stands for the method’s rate of convergence. The scaling coefficient ki is determined by the quotient of any norms of matrices Bi and or by the reciprocal of the Frobenius norm of matrix Bi. In the presented approach the condition for completing calculations has the form. Once the calculations are completed, the columns of matrix B are vectors parallel to the eigenvector corresponding to the dominant eigenvalue, which is calculated from the Rayleigh quotient. The new approach eliminates the necessity to use a starting vector, increases the rate of convergence and shortens the calculation time when compared to the classic 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 Stationary measure for three-state quantum walk

2019 ◽  
Vol 19 (11&12) ◽  
pp. 901-912
Author(s):  
Takako Endo ◽  
Takashi Komatsu ◽  
Norio Konno ◽  
Tomoyuki Terada
Keyword(s):  
Eigenvalue Problem ◽  
General Condition ◽  
Quantum Walk ◽  
Stationary Measure ◽  
One Dimension ◽  
Transfer Matrices ◽  
Initial State ◽  
Stationary Measures

We focus on the three-state quantum walk (QW) in one dimension. In this paper, we give the stationary measure in general condition, originated from the eigenvalue problem. Firstly, we get the transfer matrices by our new recipe, and solve the eigenvalue problem. Then we obtain the general form of the stationary measure for concrete initial state and eigenvalue. We also show some specific examples of the stationary measure for the three-state QW. One of the interesting and crucial future problems is to make clear the whole picture of the set of stationary measures.

A Normalized Modal Eigenvalue Approach for Resolving Modal Interaction

1997 ◽  
Vol 119 (3) ◽  
pp. 647-650 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Monte Carlo ◽  
Eigenvalue Problem ◽  
Perturbation Analysis ◽  
Material Properties ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Modal Interaction ◽  
Eigenvalue Approach ◽  
The Difference

Modal interaction refers to the way that the modes of a structure interact when its geometry and material properties are perturbed. The amount of interaction between the neighboring modes depends on the closeness of the natural frequencies, the mode shapes, and the magnitude and distribution of the perturbation. By formulating the structural eigenvalue problem as a normalized modal eigenvalue problem, it is shown that the amount of interaction in two modes can be simply characterized by six normalized modal parameters and the difference between the normalized frequencies. In this paper, the statistical behaviors of the normalized frequencies and modes are investigated based on a perturbation analysis. The results are independently verified by Monte Carlo simulations.

P-SS Algorithm for Solving the Eigenvalue Problem of Finite Element System

2013 ◽  
Vol 300-301 ◽  
pp. 1118-1121
Author(s):  
Jie Fang Wang ◽  
Wei Guang An
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
New Method ◽  
Power Method ◽  
Small System ◽  
Element System ◽  
Shrinkage Method

P-SS algorithm for solving eigenvalue problem was obtained, based on the power method and the similar shrinkage method. This algorithm can be used to not only solve all eigenvalues of small system, but also partial eigenvalues of large finite element system. The calculation program of this algorithm is universal and practical. Compared with the existing methods, the error of P-SS method is very small, and it signify that the new method is feasible and convenient.

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