Error bounds for approximate deflating subspaces for linear response eigenvalue problems

Consider the linear response eigenvalue problem (LREP) for H=[0KM0], where K and M are positive semidefinite and one of them is definite. Given a pair of approximate deflating subspaces of {K,M}, it can be shown that LREP can be transformed into one for H˜ that is nearly decoupled into two smaller LREPs upon congruence transformations on K and M that preserve the eigenvalues of H. In this paper, we establish a bound on how far the pair of approximate deflating subspaces is from a pair of exact ones, using the closeness of H˜ from being decoupled.