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Questions tagged [eigensystem]

An eigenvector of an operator is a vector such that the action of the operator is the same as multiplication by a constant, called the eigenvalue. The eigensystem of an operator is the set of all such eigenvectors and their associated eigenvalues.

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What's the most efficient way to compute the eigenvector of a dense matrix corresponding to the eigenvalue of largest magnitude?

I have a dense real symmetric square matrix. The dimension is about 1000x1000. I need to compute the first principal component and wonder what the best algorithm to do this might be. It seems that ...
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3answers
992 views

Laplacian eigenmodes on a semi-circular region with finite-difference method

The computation of eigenmodes of a semi-circular membrane reduces to the following eigenvalue problem $$\nabla^2u=k^2u\;,$$ where the region of interest is a semi-circle defined by $r\in[0,1]$ and $\...
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2answers
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Lanczos solver implementations in MATLAB/C++ give different results

I have transferred my MATLAB Lanczos solver for symmetric eigenvalue solvers to C++ with the help of Intel MKL and MTL4 libraries. I have some wrapper templates for MKL routines. However during the ...
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1answer
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What is a good stop criterion when using an iterative method to find eigenvalues?

I read this answer, and realized I have been using the difference between sucessive iterates to define a stop criterion for an iterative method of finding eigenvalues/vectors. What are good stop ...
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1answer
199 views

Is multigrid useful for finding all eigenvalues and eigenvectors of a differential equation, or only the lowest eigenvalues?

I've been considering using a multigrid method to calculate the eigenvalues of a particular PDE. I know that multigrid is extremely good at finding the least eigenvalues and their associated ...