ARPack Ritz Value and eigenvalue

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ARPack Ritz Value and eigenvalue

Postby nvinod » Tue Dec 11, 2012 12:56 pm

I have been trying to otain few eigenvalues of a large system Ax=\lambda B x where A and B are large dense matrices.

As the starting I tried running the example programme sssimp.f given in the ARPACK website. I obtained the out put as given in the website http://people.sc.fsu.edu/~jburkardt/f_s ... output.txt

It says the final Ritz values are
9.912E+02 9.198E+02 9.198E+02 9.484E+02

Obviously these are not the eigenvalues I am looking for. These values are very large for eigenvalues of the problem. If I supply the same T matrix to Matlab, it gives a different set of eigenvalues.

As I understand (correct me, if I am wrong!), there is should be a way to transform, the computed Ritz value to the approximated eigenvalues. Can someone help?
nvinod
 
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Re: ARPack Ritz Value and eigenvalue

Postby lawrence mulholland » Wed Aug 07, 2013 9:29 am

It depends how you used ARPACK.
In standard mode you will get the largest eigenvalues.
If you want smallest eigenvalues then use a shifted inverse mode with small shift.
See NAG F12 Chapter intro for a brief discussion:
http://www.nag.co.uk/numeric/fl/nagdoc_fl24/html/F12/f12intro.html#SpectralTrans
lawrence mulholland
 
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