Fast Estimation of $tr(f(A))$ via Stochastic Lanczos Quadrature

The problem of estimating the trace of matrix functions appears in applications ranging from machine learning and scientific computing, to computational biology. This paper presents an inexpensive method to estimate the trace of f(A)for cases where fis analytic inside a closed interval and Ais a symmetric positive definite matrix. The method combines three key ingredients, namely, the stochastic trace estimator, Gaussian quadrature, and...