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MathGroup Archive 2004

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Re: Accuracy problem in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49089] Re: Accuracy problem in Mathematica
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 1 Jul 2004 05:25:33 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <cbu21o$5ea$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

why not say a=1/2 instead of a=0.5 or if you love floating point numbers
say
a=0.5`100000000000000000000000000000

Regards
  Jens


aaaa wrote:
> 
> 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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