Re: Taylor expansion using the fft

[Carnë Draug]

On 8 October 2011 13:56, Fernando <address@hidden> wrote:
> Hi there
>
> Just want to post a simple Taylor expansion code based on Cauchy's integral
> formula taking
>  the contour to be a circle:
>
> function coeff = taylor(N,r,f)
>
> h = 2*pi/N;
>
> n = 0:N-1; # index of coefficients
> th = n*h;  # step length around a circle
>
> coeff = real(1./(N*(r.^n)).*fft(f(r*exp(i*th))));
>
> octave:4> taylor(16,0.5,@(x) 1./(1-x))
> ans =
>
>  Columns 1 through 8:
>
>   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000
>
>  Columns 9 through 16:
>
>   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000
>
>
> The problem is choosing the radius of your circle, to my knowledge theres no
> optimal radius r.
> Also you need to choose r such that the function f is analytic in that
> region, in the example I chose r < 1
> as there is a pole at 1.
>
> Just thought I share it since its so simple. Hope its useful.
>
> Cheers
> Fernando

Hi Fernando,

have you consider submitting to octave-forge?
http://octave.sourceforge.net/ Octave-forge is an octave sister
project that maintains several packages for octave. I'm CC'ing this
e-mail to octave-forge mailing list too.

We could include your function (and hopefully more in the future) in
there? Could you maybe suggest a package for it?

Carnë