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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 $A_0$ of $A$, and then, based on both $A$ and $A_0$, to define a sequence ${\left(A_k\right)}_{k=0}^n$ of matrices that increasingly better approximate...