On Convex Approximation by Quadratic Splines

✍ Scribed by Kamen G. Ivanov; Boyan Popov

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 221 KB
• Volume: 85
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1996.0032

✦ Synopsis

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 equally spaced knots. 1996 Academic Press, Inc.

for k=i&1, i, i+1.

(2)

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