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