A new algorithm for approximating the least concave majorant

Title:

A new algorithm for approximating the least concave majorant

Creator:

Franců, Martin, Kerman, Ron, and Sinnamon, Gord

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:241f2cc6-79ad-4104-8d70-ddfde95bcf92
uuid:241f2cc6-79ad-4104-8d70-ddfde95bcf92
issn:0011-4642

Subject:

matematika, algoritmy, mathematics, algorithms, least concave majorant, level function, spline approximation, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

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., Martin Franců, Ron Kerman, Gord Sinnamon., and Obsahuje bibliografii

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1071-1093

Source:

Czechoslovak Mathematical Journal | 2017 Volume:67 | Number:4

Harvested from:

CDK

Metadata only:

false