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It is shown that superefficient Monte Carlo computations can be carried outby using chaotic dynamical systems as non-uniform random-number generators.Here superefficiency means that the expectation value of the square of theerror decreases to 0 as 1/N^{2} with N successive observations for N->infinity, whereas the conventional Monte Carlo simulation gives the square ofthe error in the order 1/N. The order of N in the error convergence speed ofsuperefficient Monte Carlo computations does not depend on the dimensionalityof the problems. By deriving a necessary and sufficient condition for thesuperefficiency, it is shown that such high-performance Monte Carlo simulationscan be carried out only if there exists a strong correlation of chaoticdynamical variables.

Chaotic Monte Carlo Computation: A Dynamical Effect of Random-Number Generations