Krylov-aware stochastic trace estimation

We introduce an algorithm for estimating the trace of a matrix function f(A) using implicit products with a symmetric matrix A. Existing methods for implicit trace estimation of a matrix function tend to treat matrix-vector products with f(A) as a black-box to be computed by a Krylov subspace method. Like other algorithms for implicit trace estimation, our approach is based on a combination of deflation and stochastic trace estimation. However, we take a closer look at how products with f(A) are integrated into these approaches which enables several efficiencies not present in previously studied methods.