Existing results only analyze the variance of the different estimators. These algorithms are useful in applications in which there is no explicit representation of A but rather an efficient method compute z T Az given z. 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 is, all of which lead to E(1/MΣ i=1 M z i T Az i) = trace( A). We analyze the convergence of randomized trace estimators.
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