Approximations of expressions of the form If := trace(W T f(A)W ), where A ∈ Rm×m is a large symmetric matrix, W ∈ Rm×k with k ≪ m, and f is a function, can be computed without evaluating f(A) by applying a few steps of the global block Lanczos method to A with initial block-vector W . This yields a partial global Lanczos decomposition of A. We show that for suitable functions f upper and lower bounds for If can be determined by exploiting the connection between the global block Lanczos method… CONTINUE READING