I have a problem where I need to find all positive (as in the eigenvalue is positive) eigenpairs of a small (usually smaller than 60x60) nonsymmetric matrix. I can stop calculating when the eigenvalue is smaller than a certain threshold. I know that the eigenvalues are real. Any suggestions on algorithms I could use to try to squeeze out the best performance? I have to do several thousand of these decompositions, so speed is important.
Thank you in advance.
EDIT: I need to do this on the GPU in shared memory. The matrices are also not necessarily the same size. I'm not aware of any libraries that do this at the moment. Suggestions of algorithms that would be well suited to the problem would be appreciated.