The combined Shepard-Abel-Goncharov univariate operator

Teodora Cătinaş

doi:10.33993/jnaat321-730

Authors

Teodora Cătinaş "Babeş Bolyai" University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat321-730

Keywords:

Shepard-Abel-Goncharov operators, interpolation formula, degree of exactness, remainder term

Abstract views: 195

Abstract

We extend the Shepard operator by combining it with the Abel-Goncharov univariate operator in order to increase the degree of exactness and to use some specific functionals. We study this combined operator and give some of its properties. We introduce the corresponding interpolation formula and study its remainder term.

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References

Agarwal, A. and Wong, P. J. Y., Error Inequalities in Polynomial Interpolation and their Applications, Kluwer Academic Publishers, Dordrecht, 1993. DOI: https://doi.org/10.1007/978-94-011-2026-5

Cheney, W. and Light, W., A Course in Approximation Theory, Brooks/Cole Publishing Company, Pacific Grove, 2000.

Coman, Gh., The remainder of certain Shepard type interpolation formulas, Studia Univ. "Babeş--Bolyai", Mathematica, XXXII, no. 4, pp. 24-32, 1987.

Coman, Gh., Shepard-Taylor interpolation, Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca, pp. 5-14, 1988.

Coman, Gh. and Ţâmbulea, L., A Shepard-Taylor approximation formula, Studia Univ. "Babeş--Bolyai", Mathematica, XXXIII, no. 3, pp. 65-73, 1988.

Coman, Gh. and Trîmbiţaş, R., Combined Shepard univariate operators, East Jurnal on Approximations, 7, no. 4, pp. 471-483, 2001.

Coman, Gh. and Trîmbiţaş, R., Univariate Shepard-Birkhoff interpolation, Rev. Anal. Numér. Théor. Approx., 30, no. 1, pp. 15-24, 2001, http://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no1-art3

Davis, Ph. J., Interpolation and Approximation, Blaisdell Publishing Company, New York, 1963.

Dzhaparidze, K. and Janssen, R. H. P., A stochastic approach to an interpolation problem with applications to Hellinger integrals and arithmetic-geometric mean relationship, CWI Report, Amsterdam, 7, no. 3, pp. 245-258, 1994.

Sendov, B. and Andreev, A., Approximation and Interpolation Theory, in Handbook of Numerical Analysis, vol. III, ed. P. G. Ciarlet and J. L. Lions, 1994. DOI: https://doi.org/10.1016/S1570-8659(05)80017-1

Shayne, W., Refinements of the Peano kernel theorem, Numer. Funct. Anal. Optimiz., 20, nos. 1-2, pp. 147-161, 1999, https://doi.org/10.1080/01630569908816885. DOI: https://doi.org/10.1080/01630569908816885

Stancu, D. D., Coman, Gh., Agratini, O. and Trîmbiţaş, R., Numerical Analysis and Approximation Theory, vol. I, Presa Universitară Clujeană, 2001 (in Romanian).

Stancu, D. D., Coman, Gh., and Blaga, P., Numerical Analysis and Approximation Theory, vol. II, Presa Universitară Clujeană, 2002 (in Romanian).