Can i control all gradients of a spline, not just the end points?

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Edd Hirons
Edd Hirons 2014-9-22
评论： Edd Hirons 2014-9-22
PROBLEM CONTEXT: I am trying to estimate the y-coordinates of some physical system given that I know x-coordinates and the slopes/gradient of the data (will be <= 10 coordinates). I chose splines so that I do not get over fitting problems with potentially 9th order polynomials!
I would also rather use spline than pchip as I want the gradient curve to be smooth.
If for now I assume that the coordinates are equi-spaced in x and another controlling factor is that the arclength of the spline will be constant does anyone know any way to estimate (iteratively or otherwise) the y-positions? if I can gain some control over the gradients of the spline I believe I should be able to recover the possible y-positions? (i.e. swap my known information from the usual x,y, positions and use the spline to find the gradients and instead use the gradients and x positions to find the y?)
I know this is a second question but its intrinsically linked to the other problem!
Cheers,
Edd

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Matt J
Matt J 2014-9-22
The control over the derivatives that you want is possible through
http://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling
Arc-length would probably be more work. You would probably need to formulate your own constrained problem using fmincon, I imagine.

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