A new algorithm for approximating the least concave majorant

Czechoslovak Mathematical Journal

Martin Franců, Ron Kerman, Gord Sinnamon¹ 

关键词: least concave majorant;    level function;    spline approximation;   

DOI  :  10.21136/CMJ.2017.0408-16

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  The least concave majorant, $\hat F$, of a continuous function $F$ on a closed interval, $I$, is defined by$ \hat F (x) = \inf\{ G(x)G \geq F, G \text{ concave}\},\quad x \in 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 $F \in\mathcal{C}^4(I)$, it can be well-approximated on $I$ by a clamped cubic spline $S$. We show that $\hat S$ is then a good approximation to $\hat F$.We give two examples, one to illustrate, the other to apply our algorithm.

【 授权许可】

Unknown