I was wondering if someone could help me out with two small subjects. They are not a problem per se, but I'm trying to see if there's an easy solution without the need of recalculating.

In the first case, imagine I have a set of data (x and y) with a great chebyshev polynomial fit of degree N; I allready know the error and the coeficients values. Is there a direct way of fitting the same data to a lower degree chebyshev pol. - let's say for example of (N-2) degree - knowing the coeficients of the highest so I won't have to recalculate the all fit?

The second issue, is this: imagine again I have a set of data which I fitted to 4 chebyshev polynomials of a same degree N, each one fitting 1/4 of the data - I've divided the fit data in smaller segments. Can I, knowing again those coeficients, calculate directly a single one to fit all the 4 segments at once?

I hope someone can help

Thanks

Kepler