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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 2k, where k 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. © 1981 Springer-Verlag.

In this paper the authors develope a new Montecarlo method for many variables interpolation when the values of the function are known on a lattice. This technique uses cardinal splines functions. Numerical results are also reported for some problems. © 1975 Instituto di Elaborazione della Informazione del CNR