eigenvalues of many dense symmetric real matrix that are 'close' to each other
2 views (last 30 days)
Show older comments
I have to find the eigenvalues of many dense symmetric real matrix that are 'close' to each other, i.e. they are not much different. Can I speed up eig or some other code if I know the spectral decomposition of A and want to find it for a nearby B. I.e. I have A = UDU' as the spectral decomposition and want to find it for B where
B-A is small. I know this can be done for eigs with 'restarts'. But what about finding all the eigenvalues with eig?
1 Comment
David Goodmanson
on 16 Jun 2019
Edited: David Goodmanson
on 16 Jun 2019
Hi Henry,
If the eigenvalues are not too closely spaced (no repeated ones either) then a simple first order approximation gives a quick look at how much the eigenvalues change. Let A1 = B-A. The diagonal elements of
E1 = U'*A1*U
are the shifts in the eigenvalues, to first order. Perturbation theory can provide results for higher orders, using increasingly complicated expressions.
Answers (0)
See Also
Categories
Find more on Eigenvalues & Eigenvectors in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!