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derivative of cubic spline for use in nonlinear optimization

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dominik
dominik 2015-3-19
Hi
i wanna solve a functional system of nonlinear equations by collocation. To speed up the solution process i want to provide derivatives to the solver. The system includes cubic splines. So far I use Matlab's csapi to produce the cubic spline. To provide derivatives of the system, i need the derivatives of the output of csapi wrt the values of the function I interpolate at the grid points. (Either derivatives of the polynomical coefficients or even better of the evaluated polynomial). Does anyone have code for this?
Formally:
Be:
Spline=csapi(grid,functionvalues)
Interpolatedvalue=fnval(Spline,querypoint)
Then I need:
d Spline.coefs / d functionvalues
Or better:
d Interpolatedvalue / d functionvalues
Many thanks!

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