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Abstract
The problem of numerical interpolation of multivariable functions when their values are assumed to be given on discrete lattice points has been solved by the Monte Carlo method [5, 6,7]. This technique is used because the number of lattice points increases exponentially with the number of dimensions. This paper deals with numerical interpolation and differentiation of multivariable functions by a piecewise cubic polynomial in each variable. A sampling method which combines positive and negative coefficients is considered to prevent the degeneration of accuracy.