BOUNDS ON THE ERROR OF AN APPROXIMATE INVARIANT SUBSPACE FOR NONSELF-ADJOINT MATRICES

Suppose one approximates an invariant subspace of an n x n matrix in C (n x n) which in not necessarily self-adjoint. Suppose that one also h as an approximation for the corresponding eigenvalues. We consider the question of how good the approximations are. Specifically, we develop bounds on the angle between the approximating subspace and the invari ant subspace itself. These bounds are functions of the following three terms: (1) the residual of the approximations; (2) singular-value sep aration in an associated matrix; and (3) the goodness of the approxima tions to the eigenvalues.