On some bivariate interpolation procedures

Authors

  • Dimitrie D. Stancu “Babes-Bolyai” University, Cluj-Napoca, Romania
  • Ioana Taşcu North University of Baia Mare, Romania

Keywords:

bivariate interpolation, divided differences, bivariate polynomial interpolation formulas of Lagrange, Newton, Taylor, Hermite and Biermann

Abstract

In an important paper published in 1966 by the first author [10] a very general interpolation formula for univariate functions, which includes, as special cases, the classical interpolation formulae of Lagrange, Newton, Taylor and Hermite was introduced and investigated. The purpose of the present paper is to extend that formula to the two-dimensional case. The remainders are expressed by means of partial divided differences and derivatives.

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References

Biermann, O., Über näherungsweise Kubaturen, Monatsh. Math. Phys., 14, pp. 211-225,, 1903, https://doi.org/10.1007/bf01706869

Hermite, C., Sur la formule d'interpolation de Lagrange, J. Reine Angew. Math., 84, pp. 70-79, 1878, https://doi.org/10.1515/crll.1878.84.70

Johansen, P., Über osculierende Interpolation, Skand. Actuarietidskr, 14, pp. 231-237, 1931, https://doi.org/10.1080/03461238.1931.10405852

Salzer, A., A multi-point generalization of Newton's divided difference formula, Proc. Amer. Math. Soc., 13, pp. 210-212, 1962, https://doi.org/10.1090/s0002-9939-1962-0137285-1

Simonsen, W., On divided differences and osculatory interpolation, Skand. Akturietidskr., 31, pp. 157-164, 1948, https://doi.org/10.1080/03461238.1948.10404897

Stancu, D. D., On the interpolation formula of Hermite and on some applications of it (Romanian), Acad. R. P. Rom. Fil. Cluj, Stud. Cerc. Mat., 8, pp. 339-355, 1957.

Stancu, D. D., Considerations on the polynomial interpolation formulas for functions of several variables, Bul. Univ. Babeş-Bolyai, Ser. St. Nat. (Romanian), 1, pp. 43-82, 1957.

Stancu, D. D., On the integral representation of the remainder in a Taylor formula of two variables, Acad. R. P. Rom. Fil. Cluj, Stud. Cerc. Mat., 13, pp. 175-182, 1962.

Stancu, D. D., The remainder of certain linear approximation formulas in two variables, J. SIAM Numer. Anal. Ser. B, 1, pp. 137-143, 1964, https://doi.org/10.1137/0701013

Stancu, D. D., On Hermite's osculatory interpolation formula and on some generalizations of it, Mathematica (Cluj), 8(31), pp. 373-391, 1966.

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Published

2004-02-01

How to Cite

Stancu, D. D., & Taşcu, I. (2004). On some bivariate interpolation procedures. Rev. Anal. Numér. Théor. Approx., 33(1), 97–106. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no1-art13

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