How to constraint the second derivative value while fitting polynomial to set of data

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deRicaud
deRicaud 2018-7-2
评论： deRicaud 2018-7-2
Hello all,
I hope somebody can help me, knowing that I am not an expert in matlab.
Here is my problem: I need to match a polynomial of order n to a set of points (x,y). I know that the found curve has no physical meaning if the second order derivative is higher than 0 or that its sign changes (inflexions). So, I want to constraint the second order derivative of the polynomial to be always negative (not only at the ends).
I am currently using polyfit, which does not offer this option. I have found many articles on this website abount constraints on derivative, ends, but not second derivative on the entire set of points.
Basically, I want to find something always like the green curve (picture below), and not the yellow one, with a 5 order polynomial, for example.
Thank you in advance for your help.
Gaëtan.

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回答（1 个）

Matt J
Matt J 2018-7-2
编辑：Matt J 2018-7-2
This FEX package has that capability,
https://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling
See the 'concavedown' input option.
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deRicaud
deRicaud 2018-7-2
thanks, that's a nice tool! Howerver I'm a bit afraid of the complexity of it, knowing I need to run it hundreds of time in my code, and also that I might have issue explaining why I use Hermite spline. But thanks, I will dig into it to see how it is built, to see if I can find an easy way to do the concavedown.

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