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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: [mg67044] Re: Two questions (1) Sollve and (2) Precision
  • From: "Bharat Bhole" <bbhole at gmail.com>
  • Date: Thu, 8 Jun 2006 04:53:00 -0400 (EDT)
  • References: <e666j8$nbj$1@smc.vnet.net> <4486B0CA.3060002@gmail.com>
  • Sender: owner-wri-mathgroup at wolfram.com

Thanks for your help Jean-Marc. I really appreciate it. I have two comments
about your response, and it would be very helpful if things work on your
computer after taking these into account.

(1)  As I replied to all, somehow my equations were posted with an error.
The right hand sides in the two equations were 1 and 0 respectively and not
8A1 and 8A0. Also, I had used two equal signs (== and not just = when
writing the equations).

(2) For the second problem you have calculated %%%-%. So basically you are
calculating Out[5]-Out[7] in your solution below. However, I was talking
about Out[4]-Out[7], which is not zero even in your case.

Thanks very much.

 Bharat.

On 6/7/06, Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote:
>
> Bharat Bhole wrote:
> > Would appreciate if someone can point out why Mathematica is not giving
> the
> > expected output in the followng two cases.
>
> Here is what I get with Mathematica
>
> In[3]:=
> $Version
>
> Out[3]=
> 5.2 for Microsoft Windows (June 20, 2005)
>
> > (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: {}*
> >
> In[1]:=
> Solve[{64919121*x - 159018721*y == 8*A1,
>    4.18695205*^7*x - 102558961*y == 8*A0}, {x, y}]
>
> Out[1]=
>                   9                8
> {{x -> -1.27215 10  A0 + 8.20472 10  A1,
>
>                    8                8
>    y -> -5.19353 10  A0 + 3.34956 10  A1}}
>
>
> > However, the solution exists and is given by  x = 205117922, y =
> 83739041
>
> It is meaningless to speak about "The" solution if you do not tell what
> values A0 and A1 have been assigned:
>
> In[2]:=
> Solve[{64919121*x - 159018721*y == 8*A1,
>     4.18695205*^7*x - 102558961*y == 8*A0} /.
>    {x -> 205117922, y -> 83739041}, {A0, A1}]
>
> Out[2]=
> {{A1 -> 0.125, A0 -> 0.}}
>
> > 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.
> >
> >
>
> What version of Mathematica do you use? Work fine for me:
>
> In[4]:=
> 123456789123*123456789123
>
> Out[4]=
> 15241578780560891109129
>
> In[5]:=
> 123456789123*123456789123.0
>
> Out[5]=
>           22
> 1.52416 10
>
> In[6]:=
> %%-%
>
> Out[6]=
> 0.
>
> In[7]:=
> SetPrecision[123456789123*123456789123.0,50]
>
> Out[7]=
> 1.5241578780560891838464000000000000000000000000000
>
>     22
>   10
>
> In[8]:=
> %%%-%
>
> Out[8]=
> 0.
>
> In[9]:=
> $Version
>
> Out[9]=
> 5.2 for Microsoft Windows (June 20, 2005)
>
> Regards,
> Jean-Marc
>



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