polynomial fit with boundary conditions

I would like to make a polynomial fit for a vector, but imposing some boundary conditions: second derivative at the edges is zero. How can this be done?

Answer 1

[John D'Errico]

Don't!

You are describing what appears to be a spline, but will be a high order polynomial, subject to constraints. This will invariably produce crapola.

Use a spline to do the job of a spline. If you can't write that yourself, then use code from the file exchange that does it for you.

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

[DF]

That's a very nice package, however I would like to use higher order polynomials (higher than 3) and from what I've seen is not possible with SLM tools.

[Bjorn Gustavsson]

Mathworks spline toolbox has tools for splines of arbitrary order. (I thought John's SLM-tool had too.)

[DF]

Well, I have no idea how to add boundary conditions to a spline fit in Matlab. The SLM tool seemed exactly what I was looking for, but I would like to use 4th and 5th order splines.