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MathGroup Archive 2007

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Re: Coaxing N[] to work

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73387] Re: Coaxing N[] to work
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 15 Feb 2007 04:57:51 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <equo6r$in0$1@smc.vnet.net>

p at dirac.org wrote:
> Sometimes N[,] doesn't appear to work.  Like here:
> 
> 
> x = {2.0, 3.0, 5.0};
> A = { {6.0, 2.0, 1.0}, {2.0, 3.0, 1.0}, {1.0, 1.0, 1.0} };
> For[ k=0, k<15, ++k,
>    lambda = x.A.x/(x.x);
>    y = LinearSolve[A,x];
>    x = y / Norm[y,Infinity];
> ]
> N[lambda, 30]
> 
> 
> The output is:
> 
>    Out[5]= 0.578933
> 
> I was expecting 30 digits.  Why did N[] ignore my request for 30 digits?
> 

N[] cannot go from lower precision to higher. One way to deal with that 
is to use exact arithmetic as in the following example.

In[1]:=
x = {2, 3, 5};
A = {{6, 2, 1}, {2, 3, 1}, {1, 1, 1}};
Precision /@ x
Precision /@ A
For[k = 0, k < 15, ++k, lambda = x . A . x/x . x;
    y = LinearSolve[A, x]; x = y/Norm[y, Infinity]; ]
lambda
Precision[lambda]
N[lambda, 30]

Out[3]=
{Infinity, Infinity, Infinity}

Out[4]=
{Infinity, Infinity, Infinity}

Out[6]=
1102158619423970036337
----------------------
1903774504398915184457

Out[7]=
Infinity

Out[8]=
0.578933385691052787623495851172

Regards,
Jean-Marc


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