On 10/08/2011 08:36 AM, Carnë Draug wrote: > On 8 October 2011 13:56, Fernando<fdnieuwve...@gmail.com> 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.
It looks nice. But shouldn't "taking the real part" be replaced by multiplying by -i? Just in case the function has complex Taylor coefficients? ------------------------------------------------------------------------------ All of the data generated in your IT infrastructure is seriously valuable. Why? It contains a definitive record of application performance, security threats, fraudulent activity, and more. Splunk takes this data and makes sense of it. IT sense. And common sense. http://p.sf.net/sfu/splunk-d2dcopy2 _______________________________________________ Octave-dev mailing list Octave-dev@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/octave-dev
