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MathGroup Archive 2004

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A problem about numerical precision

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52609] A problem about numerical precision
  • From: Guofeng Zhang <guofengzhang at gmail.com>
  • Date: Sat, 4 Dec 2004 04:07:48 -0500 (EST)
  • Reply-to: Guofeng Zhang <guofengzhang at gmail.com>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
  I met one problem when I do some iteration: By increasing numerical
precision, the results are so different from the original one!  I
don't know what went wrong, and hope to get some answers.

The code is

delta = 1/100;
a = 9/10;
b = -3*1.4142135623730950/10;
A = { {1,0}, {b,a} };
B= { {-1,1}, {-b,b} };

f[v_,x_] := If[ Abs[ (10^20)*v-(10^20)*x]>(10^20)*delta, 1, 0 ];

M = 3000;
it = Table[0, {i,M}, {j,2} ];
it[ [1] ] = { -delta/2, (a+b)*(-delta/2) };

For[ i=1, i<M, it[ [i+1]]  = A.it[[i]]+f[ it[ [i,1] ], it[ [i,2] ]
]*B.it[ [i] ]; i++ ];
temp = Take[it, -1000];

ListPlot[ temp ];

By evaluating this, I got an oscillating orbit. I got the same using
another program. However, if I increase the numerical precision by
using
b = -3*1.4142135623730950``200/10;
to substitute the original b, the trajectory would converge to a fixed
point instead of  wandering around!

I don't know why. I am hoping for suggestions. Thanks a lot.

Guofeng


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