Hermite interpolation polynomial for many-variable functions / Kashpur. (2022)

English  Cybernetics and Systems Analysis   /     Issue (2022, 58 (3))

Kashpur O.F.
Hermite interpolation polynomial for many-variable functions

The Hermite interpolation problem in the Euclidean space is considered, where the value of the function of several variables and its first-order and second-order Gateaux differentials at the interpolation nodes are given. The problem is shown to have a unique solution of minimum norm generated by a scalar product with Gaussian measure in the finite-dimensional Euclidean space. Conditions for invariant solvability and uniqueness of the problem solution are obtained. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: Euclidean space, Gateaux differential, Hermite interpolation polynomial, Hilbert space, minimum norm, Geometry, Hilbert spaces, Polynomials, Vector spaces, Euclidean spaces, First order, Functions of several variables, Gateaux differential, Hermite interpolation, Hermite interpolation polynomial, Interpolation polynomials, Interpolation problems, Minimum norm, Second orders, Interpolation

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Kashpur O.F. (2022). Hermite interpolation polynomial for many-variable functions. Cybernetics and Systems Analysis, 58 (3), 91-100. doi: https://doi.org/10.1007/s10559-022-00472-z http://jnas.nbuv.gov.ua/article/UJRN-0001323860 [In Ukrainian].


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