[Top][All Lists]

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: stable, numerical, maclaurin series of analytic functions

From: Przemek Klosowski
Subject: Re: stable, numerical, maclaurin series of analytic functions
Date: Tue, 14 Sep 2010 14:29:30 -0400
User-agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv: Gecko/20100806 Fedora/3.1.2-1.fc13 Lightning/1.0b2 Thunderbird/3.1.2

On 09/14/2010 01:33 PM, Fotios Kasolis wrote:
If i recall correctly that was asked time ago! Given an analytic function 
f:R->R you can get an approximation of the coefficients of the maclaurin 
polynomial by a function like

This will not work for singular functions. For instance, it ll return Nans if 
your function is f(x) = 1/(1-x) and garbage if there is a singularity. An 
example is

I think this algorithm must have limited convergence radius. Your example works to around 1:

p = maclaurin (@(x) exp(sin (x)), 10);
x=0:0.01:2;plot (x, exp(sin(x)),x,pv = polyval (p, x))

a plain sin(x) seems to be valid to at least two or so:

p = maclaurin (@(x) (sin (x)), 10);
x=0:0.01:4;plot (x, (sin(x)),x,pv = polyval (p, x))

reply via email to

[Prev in Thread] Current Thread [Next in Thread]