Abstract:The trace of a matrix function f (A), most notably of the matrix inverse, can be estimated stochastically using samples x * f (A)x if the components of the random vectors x obey an appropriate probability distribution. However such a Monte-Carlo sampling suffers from the fact that the accuracy depends quadratically of the samples to use, thus making higher precision estimation very costly. In this paper we suggest and investigate a multilevel Monte-Carlo approach which uses a multigrid hierarchy to stochastica… Show more
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