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Topic: Numerical integration of polyfit coefficients
Replies: 6   Last Post: Dec 12, 2013 5:50 PM

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John D'Errico

Posts: 9,070
Registered: 12/7/04
Re: Numerical integration of polyfit coefficients
Posted: Dec 12, 2013 1:59 PM
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"Rajin " <patelr37@aston.ac.uk> wrote in message <l8ctcd$jrp$1@newscl01ah.mathworks.com>...
> Hello,
>
> I have the coefficients of a polynomial of order 12 given to me using polyfit (it was fitted to model a probability density function). I now need to use the given polynomial f(x), multiply it by x^2, and integrate it over a given boundary.
>
> I have tried using the integral function: integral(fun,xmin,xmax), where:
> fun = @(x) poly2sym(f) and f is the coefficients given by polyfit, but this doesn't work.
>
> Any ideas? Apologies if this seems trivial, I have tried everything!
>
> Thanks in advance,
> Rajin


Why use a mack truck to carry a pea to Boston?

% Assume that p12 is a 12th degree polynomial.
P12 = rand(1,13);

% Multiply by x^2, to get a 14th degree polynomial
% Remember, these are just the coefficients of the polynomial.
P14 = [P12,0,0];

% integrate
Pint = [P14./(15:-1:1),0];

Having done this, use of a 12th degree polynomial like
this is a numerical obscenity. I don't really care who gave
you the polynomial.

Polynomials are a terrible way to fit distribution functions
in general. Think of it like this: The PDF of these functions
must go to zero at +/- inf. In fact, all of the derivatives
go to zero too. No polynomial has this behavior.

What tends to happen is the polynomial fits the data
points used in the fit, but then it does execrable, nasty
things between the points. This is a common behavior
of high order polynomials, but it is especially true for
this kind of model.

So I'd go back to your source, and suggest use of a
better model. A spline is often a good idea. For example
there are very nice shape preserving splines to be found.

John



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