piecewise spline approximation

[WizardOfBoz]

My goal is to get a small number of spline functions that approximate a much
larger number of points.

I have X-Y data.  Both X and Y are nbig x 1.  If I run a cubic spline fit
using spline or interp1, I get back an nbig by 4 matrix of polynomial
coefficients.  Too many parameters for my application.  

If I create a vector Xsmall, which is nsmall x 1, and use
interp1(X,Y,XSmall), I get back interpolated Y values but not polynomial
coefficients.  I need the coefficients.

So if I have a complex waveform with hundreds of points, I'd like to figure
out how to get a series of (for example) five or at most ten spline
functions that approximate the waveform.  So I generate an Xsmall matrix
with Xsmall = [0, t1, t2, t3, ... t7];, and end up with a 7x4 matrix of
cubic spline coefficients such that the coefficients from row 1 approximate
my waveform from time 0 to t1, the second row from t1 to t2, etc...
This may be easy and obvious.  Help in pointing me in the right direction is
appreciated.
Thanks,
Wiz



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