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MathGroup Archive 2006

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Re: Problem plotting high-order Laguerre polynomials

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64235] Re: Problem plotting high-order Laguerre polynomials
  • From: AES <siegman at stanford.edu>
  • Date: Tue, 7 Feb 2006 03:36:09 -0500 (EST)
  • Organization: Stanford University
  • References: <dqn7br$l3v$1@smc.vnet.net> <ds7003$8pq$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <ds7003$8pq$1 at smc.vnet.net>,
 Paul Abbott <paul at physics.uwa.edu.au> wrote:

> > I'm doing some work which involves plotting fairly high-order Laguerre
> > polynomials, up to 200 or so.  I've been getting some very strange and
> > obviously incorrect results which seem to have to do with the order of
> > evaluation.  (I'm using Mathematica 5.0, but I've checked it in 5.2 and I

In plotting Laguerre polynomials up to orders of 60 or thereabouts 
several years, I began to get what seemed to be round-off errors -- or 
something -- zigs and zags in numerical results anyway with small 
changes in parameters.

I found I could apparently avoid this simply by using purely integer or 
rational fraction arguments (plus Pi, and the like).  E.g., to explore 
+/-0.1% variations about argument Pi/6, I'd use (999 Pi/6000), 
(1001 Pi/6000), and so on.  Purely a kludge, but seemed to work.


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