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A new algorithm for approximating the least concave majorant
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 4, pp. 1071-1093
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The least concave majorant, $\hat F$, of a continuous function $F$ on a closed interval, $I$, is defined by \[ \hat F (x) = \inf \{ G(x)\colon G \geq F,\ G \text { concave}\},\quad x \in I. \] 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 $\hat F$. \endgraf We give two examples, one to illustrate, the other to apply our algorithm.
The least concave majorant, $\hat F$, of a continuous function $F$ on a closed interval, $I$, is defined by \[ \hat F (x) = \inf \{ G(x)\colon G \geq F,\ G \text { concave}\},\quad x \in I. \] 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 $\hat F$. \endgraf We give two examples, one to illustrate, the other to apply our algorithm.
DOI : 10.21136/CMJ.2017.0408-16
Classification : 26A51, 46N10, 52A41
Keywords: least concave majorant; level function; spline approximation 
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Franců, Martin; Kerman, Ron; Sinnamon, Gord. A new algorithm for approximating the least concave majorant. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 4, pp. 1071-1093. doi: 10.21136/CMJ.2017.0408-16

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