Power Iterations and the Dominant Eigenvalue Problem

1992 ◽  
Author(s):  
Jeffery J. Leader
Keyword(s):  
Eigenvalue Problem ◽  
Dominant Eigenvalue

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.

On an analytical evaluation of the flux and dominant eigenvalue problem for the steady state multi-group multi-layer neutron diffusion equation

Kerntechnik ◽  
2014 ◽  
Vol 79 (5) ◽  
pp. 430-435 ◽  
Author(s):  
C. Ceolin ◽  
M. Schramm ◽  
B. E. J. Bodmann ◽  
M. T. Vilhena ◽  
S. de Q. B.Leite
Keyword(s):  
Steady State ◽  
Eigenvalue Problem ◽  
Diffusion Equation ◽  
Dominant Eigenvalue ◽  
Neutron Diffusion ◽  
Analytical Evaluation ◽  
Neutron Diffusion Equation

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

On eigenvalue problem of the Laplace operators for ellipsoidal areas

2018 ◽  
Vol 2018 (1) ◽  
pp. 146-154
Author(s):  
D.G. Rakhimov ◽  
◽  
Sh.M. Suyarov ◽  
Keyword(s):  
Eigenvalue Problem ◽  
Laplace Operators
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