Analysis of the monte carlo image creation by uniform separation
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
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The question "what Monte Carlo can do and cannot do efficiently" is discussed for some functional spaces that define the regularity of the input data. Important for practical computations data classes are considered: classes of functions with bounded derivatives and H篓older type conditions. Theoretical performance analysis of some algorithms with unimprovable rate of convergence is given. Estimates of complexity of two classes of algorithms - deterministic and randomized for the solution of a class of integral equations are presented.