Fit polynomial to data with prescribed second derivative

Question

Andrea 2015-1-24

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/171434-fit-polynomial-to-data-with-prescribed-second-derivative

回答： Unai San Miguel 2017-3-15

Hi!!

In desperate need for help. I have a set of data for the upper surface of an airfoil. I am trying to fit a polynomial to this set so that I can evaluate the second derivative. The current problem is that basic fitting does not produce great accuracy at the end. What I am trying desperately is to prescribe the second derivative at the left end so that this equals -0.001. I have tried csape(x,y,"second") and tried to place -0.001 everywhere but without much success. I keep getting very strange shapes or error saying that the matrices being concatenated is inconsistent.

What I am doing wrong?

Thanks everybody :(

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Matt J 2015-1-24

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/171434-fit-polynomial-to-data-with-prescribed-second-derivative#answer_165839

编辑：Matt J 2015-1-24

It might be worth having a look at this spline fitting tool,

http://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling

which provides a pretty convenient and flexible interface for constraints on the derivatives. In particular, one of the input option parameters 'xypp' lets you fix the second derivative at arbitrary points.

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

John D'Errico 2015-1-25

Of course, I might be biased in agreeing with this suggestion.

Spline models should be preferred to polynomial models anyway. Lower order polynomials are too inflexible too often, and higher order polynomials blow up too easily due to numerical problems.

请先登录，再进行评论。

Answer 2

Andrea 2015-1-24

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/171434-fit-polynomial-to-data-with-prescribed-second-derivative#answer_165827

http://uk.mathworks.com/help/curvefit/examples/cubic-spline-interpolation.html#zmw57dd0e2451

This is what I was using, the general shape is good. It only needs the second derivative correction at the endpoints and I cant get the command right

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

Answer 3

Unai San Miguel 2017-3-15

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/171434-fit-polynomial-to-data-with-prescribed-second-derivative#answer_258788

The help page for csape says that you would have to use csape(x, [-0.001, y, -0.001], 'second') or csape(x, [-0.001, y, -0.001], [2, 2]) to fit a cubic polynomial spline to (x, y) with second derivative of y wrt to x equal to -0.001 at both ends of x.

But, is this really what you want to do? Are the second derivatives the same at both ends of the upper side of your airfoil?