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The major drawback of Monte Carlo codes is that poor scaling of the accuracy of the results when the method is ``refined.'' Thus if N neutral trajectories are followed, the error in the average of any quantity computed from these trajectories is tex2html_wrap_inline64 . Since the running time T is proportional to N, the error scales as tex2html_wrap_inline70 . (This is typically worse then the direct methods used to solve partial differential equations.)

One of the goal of the study of Monte Carlo codes is to find ways to minimize this error, i.e., to minimize the multiplier in the above relations and thus to minimize the error for a given amount of CPU time.

Text books on Monte Carlo methods discussing many such techniques (see, for example, J. Spanier and E. M. Gelbard, Monte Carlo principles and neutron transport problems, Addison-Wesley, 1969). One important technique applies to scoring: the track length estimator.

Charles Karney
Fri Mar 29 16:26:47 EST 1996