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MathGroup Archive 2004

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Accuracy problem in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49061] Accuracy problem in Mathematica
  • From: "aaaa" <aaa at huji.ac.il>
  • Date: Wed, 30 Jun 2004 05:34:09 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,

I'm having a problem with a calculation in Mathematica which I can't 
solve. I have an expression which I know to be (from analytical reasons) 
always between 0 and 1. It's a function of a and n ( n being natural and 
a rational) and it looks like this:

1/(1-a^2)^n +

Sum[((2*n - k - 1)!/((n - 1)!*(n - k)!*2^(2*n - k)))*(1/(1 + a)^k - 1/(1 
- a)^k), {k, 1, n}]

     

Let's say a=0.5.

Now, when I try to calculate for small n, it's ok. When calculating for 
large n's (around 400 and above) I'm starting to get wrong results (the 
number not being between 0 and 1). The problem is that the first term 
(the first line before the sum) is VERY VERY close to the negative of 
the second term (the sum), and it's getting closer as n grows. When 
using large n's, Mathematica says they are the same number or even that 
the last term is bigger (which means the whole expression becomes 
negative) - which is wrong. It's a matter of accuracy, and I'm not sure 
how I can fix it.

Can anybody help me?



Itamar


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