Re: Least Squares fit to Legendre Polynomial

Fred wrote:
>
> Hello
>
> I'm doing a physics experiment in which we measure the angular correlation
> of scattered gamma rays.
> The theoretical angular distribution is expressed in terms of a truncated
> series of Legendre Polynomials and one objective of the experiment is to
> compare theoretical and experimental values for the coefficients in this
> series.
>
> So, if I have a set of data points V_i, U_i (where Ui = cos(theta_i), how
> can I find the coefficients A_n which minimise the least squares error
> between my data points and Sum (A_n * P_n(U_i)) where P_n is the Legendre
> Polynomial of degree n and n goes from 0 to 4.
>
> Any help or pointers would be greatly appreciated.
> (Any Matlab code would be really good)
>
> Thanks
> Fred

Let me recommend the truly outstanding lecture notes by (um, er, blush) me:

http://galileo.phys.virginia.edu/classes/551.jvn.fall01/551Notes.htm

In particular look at the chapter "Representation of Functions".


--
Julian V. Noble
Professor Emeritus of Physics

http://galileo.phys.virginia.edu/~jvn/

"For there was never yet philosopher that could endure the
toothache patiently."

-- Wm. Shakespeare, Much Ado about Nothing. Act v. Sc. 1.
.

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