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Solving Hermite Interpolation Problem in Finite-Dimensional Euclidean Space


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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  1. W. A. Porter, “An overview of polynomic system theory,” Proc. IEEE, Special Issue on System Theory, Vol. 64, No. 1, 18–26 (1976).

    MathSciNet  Google Scholar 

  2. K. I. Babenko, Fundamentals of Numerical Analysis [in Russian], NITs Regulyarnaya i Khaoticheskaya Dinamika, Moscow–Izhevsk (2002).

  3. P. Kergin, “Interpolation of Ck functions,” PhD Thesis, University of Toronto (1978).

  4. K. C. Chung and T. H. Yao, “On latticies admitting unique Lagrange representations,” SIAM J. Numer. Anal., Vol. 14, Iss. 4, 735–743 (1977).

  5. V. L. Makarov and V. V. Khlobystov, Foundations of Polynomial Operator Interpolation Theory [in Russian], Institute of Mathematics of the NAS of Ukraine, Kyiv (1999).

  6. V. V. Khlobystov and O. F. Kashpur, “An Hermite operator interpolant in the Hilbert space that is asymptotically exact on polynomials,” Visnyk Kyiv. Univ., Ser. Fiz.-Mat. Nauky, No. 2, 437–448 (2005).

  7. A. D. Egorov, P. I. Sobolevskii, and L. A. Yanovich, Approximate Methods for Calculation of Continual Integrals [in Russian], Nauka i Tekhnika, Minsk (1985).

  8. I. I. Gikhman and A. V. Skorokhod, Theory of Random Processes [in Russian], Vol. 1, Nauka, Moscow (1971).

  9. V. L. Makarov, V. V. Khlobystov and L. A. Yanovich, Methods of Operator Interpolation, Institute of Mathematics of the NAS of Ukraine, Kyiv, Vol. 83 (2010).

  10. F. R. Gantmacher, The Theory of Matrices [in Russian], Fizmatlit, Moscow (2010).

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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).

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