Method Of Statistical Testing Monte Carlo Method | Yu. A. Shreider

The present volume of the Mathematical Reference Library is devoted to the so-called method of statistical trials (the Monte Carlo method). In contrast with the earlier volumes, which were devoted to the classical divisions of mathematics and a sharply delineated subject matter with well-established terminology and traditions of exposition, the mathematical methods examined in the present volume have been developed only in the last thirteen

years.*

These methods, which are applied in the most varied fields

of computational mathematics, are unified by a single common idea.

They are based on the principle of simulating a statistical experiment by computational techniques and recording the numeri­ cal characteristics obtained from this experiment. Therefore, all these methods are united under the common name of statistical trials or the Monte Carlo method. The solution of numerical problems by this method is closer in spirit to physical ex­ periments than to classical computational methods. Error in the Monte Carlo method cannot be sufficiently well evaluated in advance and, as a rule, is found by determining the mean squares for the simulated quantities. In a number of cases the solution cannot be accurately reproduced. The solution is stable

with respect to single errors in operation of the given electronic computer.

It is the purpose of the present volume to show the fundamental distinctive features of the Monte Carlo method, giving a suf­ ficiently thoroughdiscussion ofthefacilities andtypicalprocedures employed and the principal regions of application.