poly and polyval for large vectors...

Hello,

I need to get the equation of the polynomial through 50 points... a 49th order should make a perfect fit. This doesn't do it:

(load x and y vectors with unique monotonically increasing values...then:)

            [p,S,mu] = polyfit(x,y,49);
            yp = polyval(p,x);

There is some advice to use "centering and scaling" from the warning message. Using HELP I see:

    [P,S,MU] = polyfit(X,Y,N) finds the coefficients of a polynomial in
    XHAT = (X-MU(1))/MU(2) where MU(1) = MEAN(X) and MU(2) = STD(X). This
    centering and scaling transformation improves the numerical properties
    of both the polynomial and the fitting algorithm.

I'm not sure how to follow that advice. Is the an example where a large number of points is used with a poly that should capture them perfectly?

Thanks for helping.

Answer 1

[Guillaume]

The documentation of polyfit has an example of how to use the centering and scaling option. You need to use that returned mu in polyval for it to make sense:

[p, ~, mu] = polyfit(x, y, 49);
yp = polyval(p, x, [], mu);

This is way outside my area of expertise but I believe that fitting a 49 degree polynomial to 50 points is not an appropriate way to fit data. You probably would be better off fitting splines.

[David Pesetsky]

That gives MUCH better answers... if I use an order of 50 rather than 49. I have 50 points, so I'd think that's slightly over-specified... but good for now.

I'll need to check out splines if poly doesn't work.

Thanks!