I have a symmetric indefinite matrix, $H$. I also have a routine that can compute the algebraically smallest eigenvalues of a symmetric indefinite matrix. I would like to compute the eigenvalues with smallest magnitude using my existing code.
One way I can do this is to use my routine to compute the algebraically smallest eigenpairs of $H^2$. Then I can use Rayleigh quotients to figure the smallest magnitude eigenvalues of $H$. This works great but is very slow since $cond(H^2) = cond(H)^2$.
Is there a better way?