Subspace iteration accelrated by using Chebyshev polynomials for eigenvalue problems with symmetric matrices

1976 ◽  
Vol 10 (4) ◽  
pp. 935-944 ◽  
Author(s):  
Yoshiyuki Yamamoto ◽  
Hideomi Ohtsubo
Keyword(s):  
Chebyshev Polynomials ◽  
Eigenvalue Problems ◽  
Symmetric Matrices ◽  
Subspace Iteration

A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Cun-Qiang Miao
Keyword(s):  
Convergence Rate ◽  
Chebyshev Polynomials ◽  
Numerical Experiments ◽  
Eigenvalue Problems ◽  
Cubic Convergence ◽  
Davidson Method ◽  
Filtering Technique ◽  
Matrix Vector ◽  
Three Term Recurrence Relation ◽  
Symmetric Eigenvalue Problems

AbstractFor symmetric eigenvalue problems, we constructed a three-term recurrence polynomial filter by means of Chebyshev polynomials. The new filtering technique does not need to solve linear systems and only needs matrix-vector products. It is a memory conserving filtering technique for its three-term recurrence relation. As an application, we use this filtering strategy to the Davidson method and propose the filtered-Davidson method. Through choosing suitable shifts, this method can gain cubic convergence rate locally. Theory and numerical experiments show the efficiency of the new filtering technique.

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 Acceleration of Hessenberg reduction for nonsymmetric matrix.

2021 ◽  
Author(s):  
Hesamaldin Nekouei
Keyword(s):  
Hybrid Algorithm ◽  
Eigenvalue Problems ◽  
Symmetric Matrices ◽  
Real Matrix ◽  
Great Efficiency ◽  
Matrix Size ◽  
Hessenberg Form ◽  
Large Matrix ◽  
Speed Up ◽  
Nonsymmetric Matrix

The worth of finding a general solution for nonsymmetric eigenvalue problems is specified in many areas of engineering and science computations, such as reducing noise to have a quiet ride in automotive industrial engineering or calculating the natural frequency of a bridge in civil engineering. The main objective of this thesis is to design a hybrid algorithm (based on CPU-GPU) in order to reduce general non-symmetric matrices to Hessenberg form. A new blocks method is used to achieve great efficiency in solving eigenvalue problems and to reduce the execution time compared with the most recent related works. The GPU part of proposed algorithm is thread based with asynchrony structure (based on FFT techniques) that is able to maximize the memory usage in GPU. On a system with an Intel Core i5 CPU and NVIDA GeForce GT 635M GPU, this approach achieved 239.74 times speed up over the CPU-only case when computing the Hessenberg form of a 256 * 256 real matrix. Minimum matrix order (n), which the proposed algorithm supports, is sixteen. Therefore, supporting this matrix size is led to have the large matrix order range.

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