A bayes method for the numerical solution of nonlinear equations

A new method based on the statistical (Bayes) approach is described for the numerical solution of a system of nonlinear equations with the a priori specified domain of existence of real roots. This method does not require that the first approximation should be known and, in general, does not presuppose the use of iterations; in addition, it provides a method for determining several vectors of roots for the system of equations based on the successive partition of the a priori specified domain. The amount of computation involved in the method is small if the left-hand side of the system of equations is fixed while the right-hand side varies, for example, as a result of a series of observations. The method may be used for the numerical solution of applied problems of nonlinear programming and certain problems of discrete optimal control.