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.
Best Answer
Don't know if this would work with a complex matrix, but partial pivoting may help out (LU factorization).
lu(A)http://www.mathworks.com/help/matlab/ref/lu.html