Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix

We analyze the convergence of randomized trace estimators. Starting at 1989, several algorithms have been proposed for estimating the trace of a matrix by 1/MΣ i =1 M z i T Az i , where the z i are random vectors; different estimators use different distributions for the z i s, all of which lead to E (1/MΣ i =1 M z i T Az i ) = trace( A ). These algorithms are useful in applications in which there is no explicit representation of A but rather an...