Univariate Shepard-Birkhoff Interpolation
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https://doi.org/10.33993/jnaat301-677Abstract
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
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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.
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