DIVIDED DIFFERENCES AND POLYNOMIAL CONVERGENCES

Title & Authors
DIVIDED DIFFERENCES AND POLYNOMIAL CONVERGENCES
PARK, SUK BONG; YOON, GANG JOON; LEE, SEOK-MIN;

Abstract
The continuous analysis, such as smoothness and uniform convergence, for polynomials and polynomial-like functions using differential operators have been studied considerably, parallel to the study of discrete analysis for these functions, using difference operators. In this work, for the difference operator $\small{{\nabla}_h}$ with size h > 0, we verify that for an integer $\small{m{\geq}0}$ and a strictly decreasing sequence $\small{h_n}$ converging to zero, a continuous function f(x) satisfying \$\${\nabla}_{h_n}^{m+1}f(kh_n)
Keywords
Convergence;Polynomial;Divided Difference Equation;Subdivision Scheme;
Language
English
Cited by
References
1.
N. Dyn, Subdivision schemes in computer-aided geometric design, in : W. A. Light (Ed.), Advances in numerical anaysis II: Wavelets, Subdivision Algorithms and Rational Basis Functions, Clarendon Press, Oxford, 1992, 36-104.

2.
J. Warren and H. Weimer, Subdivision Methods for Geometric Design: A Constructive Approach, Morgan Kaufmann, 2001.

3.
E. Kreyszig, Introductory Functional Analysis with Application, John Wiley & Sons, New York, 1978.

4.
P. Davis, Interpolation and Approximation, Blaisdell, New York, 1963.

5.
P. Koch and T. Lyche, Construction of exponential tension B-splines of arbitrary order, in : P. Laurent, A. LeMehaute, and L. Schumaker (Eds.), Curves and Surfaces, Academic Press, New York, 1991.