poly and polyval for large vectors...

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David Pesetsky
David Pesetsky 2018-7-23
评论： David Pesetsky 2018-7-23
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.

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Guillaume
Guillaume 2018-7-23
编辑：Guillaume 2018-7-23
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.
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David Pesetsky
David Pesetsky 2018-7-23
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!

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