UDC 517.988
HERMITE INTERPOLATION POLYNOMIAL FOR MANY-VARIABLE FUNCTIONS
Abstract. In this paper we consider solving of the Hermite interpolation problem in Euclidean space, in the case whetr the values
of the many-variable function and the values of its Gateaux differential of the first and second order at the interpolation nodes are given.
It is shown that the problem has a unique solution of minimum norm generated by a scalar product with a Gaussian measure.
The conditions of invariant solvability and uniqueness of the solution of the problem are obtained.
Keywords: Hermit interpolation polynomial, Gateaux differential, Hilbert space, Euclidean space, minimum norm.
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