Approximation of multivariable functions with respect to random points less than 2k,k dimension of space

Summary The problem of the numerical approximation of multivariable functions has been solved by the Monte Carlo method when the data points are assumed to be given on discrete lattice points [5, 8, 2]. When the data points are randomly distributed and very numerous there are some results in the literature [3, 6] but if the number of the points is less than 2^k, wherek is the dimension of the space, it is very difficult to develop approximation formulas. This paper gives a solution to this problem by local approximations.