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MathGroup Archive 2006

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Re: Two questions (1) Sollve and (2) Precision

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67072] Re: Two questions (1) Sollve and (2) Precision
  • From: "ben" <benjamin.friedrich at gmail.com>
  • Date: Thu, 8 Jun 2006 04:54:48 -0400 (EDT)
  • References: <e666j8$nbj$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Bharat,

(1)

Try == instead of = in your equations.

(2)

Numerical results are usually printed with only a few digits,
not with full accuracy.

Bye
Ben

Bharat Bhole schrieb:

> Would appreciate if someone can point out why Mathematica is not giving the
> expected output in the followng two cases.
>
> (1) I was trying to solve the follwing two linear equations using 'Solve'.
>
>
> *In: Solve[{64919121*x-159018721*y=8A1,41869520.5*x-102558961*y=8A0},{x,y}]*
>
> *Out: {}*
>
> However, the solution exists and is given by  x = 205117922, y = 83739041
>
> Why is Mathematica unable to solve this simple linear equation? Am I doing
> something wrong?
>
>
>
> (2) I suppose that the default precision for numerical calculations is
> MachinePrecision which is less than 16. If I increase the precision, should
> I not get more accurate results? The example below seems to contradict that.
>
> (i) Exact Calculation
>
> *In[1]: 123456789123 * 123456789123*
>
> *Out[1]: 15241578780560891109129*
>
> (ii) Numerical Calculation with Default Precision
>
> *In[2]: 123456789123 * 123456789123.0*
>
> *Out[2]: 1.52416 =D7 10^22*
>
> (iii) Numerical Calcuation with a higher precision.
>
> *In[3]:SetPrecision[ 123456789123 * 123456789123.0 , 50 ]*
>
> *Out[3]: 1.5241578780560891838464000000000000000000000000000 x 10^22*
>
> Now if I calculate Out[1]-Out[2], I get zero.
>
> But if I calculate Out[1]-Out[3], I get  -729335.000000000000000000000000000
> .
>
> This seems to suggest that calculation 2 is more accurate even though it has
> smaller precision. Where am I making a mistake?
> 
> Thanks very much for your help.


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