A mixed method of subspace iteration for Dirichlet eigenvalue problems

1997 ◽  
Vol 4 (1) ◽  
pp. 243-248
Author(s):  
Gyou -Bong Lee ◽  
Sung -Nam Ha ◽  
Bum -Il Hong
Keyword(s):  
Mixed Method ◽  
Eigenvalue Problems ◽  
Dirichlet Eigenvalue ◽  
Subspace Iteration

scholarly journals EIGENVALUE ESTIMATES FOR HIGHER ORDER ELLIPTIC EQUATIONS

1994 ◽  
Vol 25 (3) ◽  
pp. 267-278
Author(s):  
HSU-TUNG KU ◽  
MEI-CHIN KU ◽  
XIN-MIN ZHANG
Keyword(s):  
Lower Bound ◽  
Elliptic Equations ◽  
Eigenvalue Problems ◽  
Higher Order ◽  
Bounded Domains ◽  
Dirichlet Eigenvalue ◽  
Eigenvalue Estimates

In this paper, we obtain good lower bound estimates of eigenvalues for various Dirichlet eigenvalue problems of higher order elliptic equations on bounded domains in $\mathbb{R}^n$.

Subspace Iteration for Nonsymmetric Eigenvalue Problems Applied to the λ-Eigenvalue Problem

1993 ◽  
Vol 115 (3) ◽  
pp. 244-252 ◽  
Author(s):  
Matthias G. Döring ◽  
Jens Chr. Kalkkuhl ◽  
Wolfram Schröder
Keyword(s):  
Eigenvalue Problem ◽  
Eigenvalue Problems ◽  
Subspace Iteration

Subspace Iteration for Eigen-Solution of Fluid-Structure Interaction Problems

1987 ◽  
Vol 109 (2) ◽  
pp. 244-248 ◽  
Author(s):  
I.-W. Yu
Keyword(s):  
Structural Dynamics ◽  
Iteration Method ◽  
Eigenvalue Problems ◽  
Fluid Structure Interaction ◽  
Fluid Pressure ◽  
Real Form ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Subspace Iteration ◽  
Symmetric Eigenvalue Problems

The subspace iteration method, commonly used for solving symmetric eigenvalue problems in structural dynamics, can be extended to solve nonsymmetric fluid-structure interaction problems in terms of fluid pressure and structural displacement. The two cornerstones for such extension are a nonsymmetric equation solver for the inverse iteration and a nonsymmetric eigen-procedure for subspace eigen-solution. The implementation of a nonsymmetric equation solver can easily be obtained by modifying the existing symmetric procedure; however, the nonsymmetric eigen-solver requires a new procedure such as the real form of the LZ-algorithm. With these extensions the subspace iteration method can solve large fluid-structure interaction problems by extracting a group of eigenpairs at a time. The method can generally be applied to compressible and incompressible fluid-structure interaction problems.

scholarly journals Multiple positive solutions for discrete p-Laplacian equations with potential term

2013 ◽  
Vol 7 (2) ◽  
pp. 327-342 ◽  
Author(s):  
Jong-Ho Kim ◽  
Jea-Hyun Park ◽  
June-Yub Lee
Keyword(s):  
Positive Solutions ◽  
Eigenvalue Problems ◽  
Existence Of Solutions ◽  
Growth Conditions ◽  
Multiple Positive Solutions ◽  
Source Terms ◽  
Dirichlet Eigenvalue ◽  
Nonlinear Source ◽  
Potential Term ◽  
Laplacian Equations

We study the existence of solutions to nonlinear discrete boundary value problems with the discrete p-Laplacian, potential, and nonlinear source terms. Using variational methods, we demonstrate that there exist at least two positive solutions. The existence strongly depends on the smallest positive eigenvalue of Dirichlet eigenvalue problems and the growth conditions of the source terms.

Numerical methods for large eigenvalue problems

Acta Numerica ◽  
2002 ◽  
Vol 11 ◽  
pp. 519-584 ◽  
Author(s):  
Danny C. Sorensen
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Large Scale ◽  
Eigenvalue Problems ◽  
Large Eigenvalue ◽  
Considerable Progress ◽  
Krylov Methods ◽  
The Past ◽  
Subspace Iteration ◽  
Nonsymmetric Matrices

Over the past decade considerable progress has been made towards the numerical solution of large-scale eigenvalue problems, particularly for nonsymmetric matrices. Krylov methods and variants of subspace iteration have been improved to the point that problems of the order of several million variables can be solved. The methods and software that have led to these advances are surveyed.

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