Publication at Faculty of Mathematics and Physics |
2017
Abstract
The least concave majorant, (F)over-cap, of a continuous function F on a closed interval, I, is defined by (F)over-cap(x) = inf{G(x): G >= F, G concave}, x is an element of I. We present an algorithm, in the spirit of the Jarvis March, to approximate the least concave majorant of a differentiable piecewise polynomial function of degree at most three on I.
Given any function F is an element of C-4(I), it can be well-approximated on I by a clamped cubic spline S. We show that (S)over-cap is then a good approximation to (F)over-cap.
We give two examples, one to illustrate, the other to apply our algorithm.