How to use `ARSymStdEig` in the shift-invert mode?

[m-reuter]

How to use `ARSymStdEig` in the shift-invert mode?

[m-reuter]

Hi, I used shift invert to solve a generalized symmetric sparse problem, similar to https://github.com/m-reuter/arpackpp/blob/master/examples/superlu/sym/lsymgshf.cc
I had the first eigenvalue be 0, which lead to instabilities, so I moved it out of the way slightly (using sigma to shift the problem away from zero).
In your case, I don't know. You can play around with inverting (so that eigenvalues increase) and shift so that all are above zero.
About the missing method in ARdsNonSymMatrix, not everything is completely implemented it seems. I have never used non symmetric matrices, so not sure if this was omitted on purpose or if it is just missing. Sorry I can't be more helpful.

[dburov190]

No worries! And thanks for a quick reply.

I understand why mathematically it should work, I'm just wondering if there is a ready-made solution (it seems not). I think they left out those implementations on purpose (which is good), but didn't provide a convenient interface to implement it yourself (not good).

The manual says the (A - sigma * I)^(-1) * v solver is automatically provided by ARPACK++ for ARluSymStdEig, but it uses LU-decomposition. This is too memory-hungry and inefficient for large matrices, I believe? I'd probably use some sort of an iterative solver.

I wonder if there's any theory for how to combine IRAM and an iterative solver that is also based on Krylov subspaces. Because it seems to me that something like MINRES could benefit greatly from reusing the already computed Krylov subspaces.