WHAT I FACE: I'm dealing with a complex matrix of very high condition number and I have to solve the eigenvalue and eigenfunction of it. But in Matlab, I got the problem that the results are not converging with increasing resolution number, so these results are not reliable.
WHAT I NEED: I in fact only need to get one eigenvalue and its associated eigenfunction (largest real part), so I tried with eigs in Matlab, but it says that "znaupd did not find any eigenvalues to sufficient accuracy", even though I have relaxed the tolerance to a very high value.
WHAT I HAVE TRIED: As I said, I have tried eig and eigs in Matlab, but these two commands can't give me accurate results.
What should I do if I want to solve this kind of problem (to get one eigenvalue of a very-high-condition-number matrix)? Should I move to other solvers other than Matlab? I think Matlab is already the best we can do, right?
Thanks. Any discussion will be appreciated.
By the way, I'm using the collocation spectral method for the grid discretization.