Univariate Shepard-Birkhoff Interpolation

Authors

  • Gheorghe Coman Babeş-Bolyai University, Cluj-Napoca, Romania
  • Radu T. Trîmbiţaş Babeş-Bolyai University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat301-677
Abstract views: 203

Abstract

In this paper we study the univariate Shepard-Birkho operators. We give an error estimation for the aproximation with these operators and some examples and graphs.

Downloads

Download data is not yet available.

References

G. Criscuolo and G. Mastroianni, Estimates of the Shepard interpolatory procedure, Acta Math. Hung., 61 (1993), 79-91,https://doi.org/10.1007/bf01872100 DOI: https://doi.org/10.1007/BF01872100

B. Della Vecchia and G. Mastroianni, Pointwise simultaneous approximation by rational operators, J. Approx. Theory, 65 (1991), 140-150, https://doi.org/10.1016/0021-9045(91)90099-v DOI: https://doi.org/10.1016/0021-9045(91)90099-V

B. Della Vecchia and G. Mastroianni, Pointwise estimates of rational operators based on general distribution of knots, Facta Universitatis (Niš), Ser. Math. Inform., 6 (1991), 63-72.

B. Della Vecchia and G. Mastroianni, On functions approximations by Shepard-type operators - a survey, Approximation theory, wavelets and applications (Maratea, 1994) 335-346, NATO Adv. Sci. Inst. Ser. C, Math. Phys. Sci., 454, Kluwer Acad. Publ., Dordrecht, 1995, https://doi.org/10.1007/978-94-015-8577-4_20 DOI: https://doi.org/10.1007/978-94-015-8577-4_20

Gh. Coman and R. Trîmbiţaş, Shepard operators of Lagrange-type, Studia Univ. "Babeş-Bolyai", Mathematica, 42 (1997), 75-83.

Gh. Coman and L. Ţâmbulea, A Shepard-Taylor approximation formula, Studia Univ. "Babeş--Bolyai", Mathematica, 33 (1988), 65-73.

Gh. Coman and R. Trîmbiţaş, Bivariate Shepard interpolation, "Babeş--Bolyai" University, Faculty of Mathematics and Computer Science, Seminar on Numerical and Statistical Calculus, Preprint No. 1 (1999), 41-83.

Gh. Coman, Shepard operators of Hermite-type, Rev. Anal. Numér. Théor. Approx, 26 (1997), 33-38.

Gh. Coman, Shepard operators of Birkhoff-type, Calcolo, 35 (1998), 197-204, https://doi.org/10.1007/s100920050016 DOI: https://doi.org/10.1007/s100920050016

Gh. Coman, Numerical Analysis, Libris Publishers, Cluj-Napoca, Romania, 1994 (in Romanian).

R. Farwig, Rate of convergence of Shepard's global interpolation formula, Math. Comp., 46 (1986), 577-590, https://doi.org/10.1090/s0025-5718-1986-0829627-0 DOI: https://doi.org/10.1090/S0025-5718-1986-0829627-0

Gh. Coman and R. Trîmbiţaş, Bivariate Shepard interpolation in MATLAB, Proc. of "Tiberiu Popoviciu" Itinerant Seminar, Cluj-Napoca 2000.

D. Shepard, A two dimensional interpolation function for irregularly spaced data, Proc. 23rd Nat. Conf. ACM, (1968), 517-523. DOI: https://doi.org/10.1145/800186.810616

R. Trîmbiţaş, Univariate Shepard-Lagrange interpolation, submitted.

Downloads

Published

2001-02-01

How to Cite

Coman, G., & Trîmbiţaş, R. T. (2001). Univariate Shepard-Birkhoff Interpolation. Rev. Anal. Numér. Théor. Approx., 30(1), 15–24. https://doi.org/10.33993/jnaat301-677

Issue

Section

Articles