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Solving Hermite Interpolation Problem in Finite-Dimensional Euclidean Space

Abstract

The Hermite problem in the Euclidean space is considered, where the value of a function of several variables and its first-order Gateaux differentials at the interpolation nodes are given. The problem is shown to have a unique minimum-norm solution in the case of underdefiniteness. Conditions for invariant solvability and uniqueness of the problem solution are obtained.

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Correspondence to O. F. Kashpur.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 2, March–April, 2022, pp. 118–127.

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Kashpur, O.F. Solving Hermite Interpolation Problem in Finite-Dimensional Euclidean Space. Cybern Syst Anal 58, 259–267 (2022). https://doi.org/10.1007/s10559-022-00458-x

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  • DOI: https://doi.org/10.1007/s10559-022-00458-x

Keywords

  • Hermite interpolation polynomial
  • Gateaux differential
  • Hilbert space
  • Euclidean space
  • minimum norm