Analysis of Subspace Iteration for Eigenvalue Problems with Evolving Matrices

2016 ◽  
Vol 37 (1) ◽  
pp. 103-122 ◽  
Author(s):  
Yousef Saad
Keyword(s):  
Eigenvalue Problems ◽  
Subspace Iteration

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.

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.

Solving Huge Gyroscopic Eigenproblems With AMLS and Subspace Iteration

2012 ◽  
Author(s):  
Heinrich Voss ◽  
Jiacong Yin ◽  
Pu Chen
Keyword(s):  
Structural Analysis ◽  
Orthogonal Projection ◽  
Eigenvalue Problems ◽  
Projection Methods ◽  
Powerful Technique ◽  
Subspace Iteration

The Automated Multilevel Sub-structuring (AMLS) method is a powerful technique for computing a large number of eigenpairs with moderate accuracy for huge definite eigenvalue problems in structural analysis. It also turned out to be a useful tool to construct a suitable ansatz space for orthogonal projection methods for gyroscopic problems. This paper takes advantage of information gained from AMLS to improve the obtained eigenpairs via a small number of subspace iteration steps.

Convergence and Preconditioning of Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

2020 ◽  
Vol 20 (2) ◽  
pp. 343-359
Author(s):  
Rayan Nasser ◽  
Miloud Sadkane
Keyword(s):  
Eigenvalue Problems ◽  
Matrix Pencil ◽  
Linear Rate ◽  
Subspace Iteration ◽  
Matrix Anal ◽  
Small Constant ◽  
Large Matrix ◽  
Generalized Eigenvalue Problems ◽  
The One ◽  
Inner Iteration

AbstractThis paper focuses on the inner iteration that arises in inexact inverse subspace iteration for computing a small deflating subspace of a large matrix pencil. First, it is shown that the method achieves linear rate of convergence if the inner iteration is performed with increasing accuracy. Then, as inner iteration, block-GMRES is used with preconditioners generalizing the one by Robbé, Sadkane and Spence [Inexact inverse subspace iteration with preconditioning applied to non-Hermitian eigenvalue problems, SIAM J. Matrix Anal. Appl. 31 2009, 1, 92–113]. It is shown that the preconditioners help to maintain the number of iterations needed by block-GMRES to approximately a small constant. The efficiency of the preconditioners is illustrated by numerical examples.

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