On the Subspace Projected Approximate Matrix method

We provide a comparative study of the Subspace Projected Approximate Matrix method, abbreviated SPAM, which is a fairly recent iterative method of computing a few eigenvalues of a Hermitian matrix A. It falls in the category of inner-outer iteration methods and aims to reduce the costs of matrix-vector products with A within its inner iteration. This is done by choosing an approximation A0 of A, and then, based on both A and A0, to define a sequence (Ak)k=0n of matrices that increasingly better approximate A as the process progresses. Then the matrix Ak is used in the kth inner iteration instead of A.