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
β¦ LIBER β¦
Convex Approximation by Quadratic Splines
β Scribed by Y.K. Hu
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 473 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
β¦ Synopsis
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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