Liebe Mitarbeiter des INS, im Rahmen unseres Forschungsseminars "Mathematics of Computation" gibt es am Donnerstag einen Vortrag von Mario Ullrich (JKU, Linz) "On a Monte Carlo method for smooth functions" Die Vorträge finden morgen, am Donnerstag, den 31.03. um 13:00 Uhr s.t. im Raum 6.020 WE6 statt. Mit den besten Grüßen Daniel Peterseim, Tino Ullrich, André Uschmajew Abstract: We present error bounds for a lattice rule for numerical integration equipped with a random shift and a random dilation of the point set. In particular, we show that the error of this method can be bounded by the L_2-norm of the Fourier transform away from the origin. This implies, e.g., that the worst-case error for mixed Sobolev spaces H^s_p with p\ge2 and s>0 is of the order n^{-s-1/2} without additional log-factors. Hence, the order is independent of the dimension. This seems to be the first non-trivial example where randomization can improve the performance of an algorithm by more than n^{-1/2}. _______________________________________________ Ins-mitarbeiter mailing list Ins-mitarbeiter@ins.uni-bonn.de https://mail.ins.uni-bonn.de/mailman/listinfo/ins-mitarbeiter