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Convex Approximation by Splines

โœ Scribed by Beatson, R. K.

Book ID
118198610
Publisher
Society for Industrial and Applied Mathematics
Year
1981
Tongue
English
Weight
1015 KB
Volume
12
Category
Article
ISSN
0036-1410

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Given a convex function \(f\) without any smoothness requirements on its derivatives, we estimate its error of approximation by \(\mathbf{C}^{1}\) convex quadratic splines in terms of \(\omega_{3}(f, 1 / n)\). C 1993 Academic Press, Inc.

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In a recent paper by Hu it is proved that for any convex function f there is a C 1 convex quadratic spline s with n knots that approximates f at the rate of | 3 ( f, n &1 ). The knots of the spline are basically equally spaced. In this paper we give a simple construction of such a spline with equall