Accelerating Matrix Trace Estimation by Aitken's Δ² Process

Abstract

We present an algorithm to estimate the trace of symmetric matrices that are available only via Matrix-Vector multiplication. The proposed algorithm constructs a series of trace estimates by applying the probing technique with an increasing number of vectors. These estimates are then treated as a converging sequence whose limit is the sought matrix trace, and we apply Aitken's Δ2 process to accelerate its convergence to the trace limit. Numerical experiments performed on covariance matrices demonstrate the competitiveness of the proposed scheme versus probing and randomized trace estimators.