       A problem of numerical precision

• To: mathgroup at smc.vnet.net
• Subject: [mg52610] A problem of numerical precision
• From: Guofeng Zhang <guofengzhang at gmail.com>
• Date: Sat, 4 Dec 2004 04:07:49 -0500 (EST)
• References: <200412030815.DAA25377@smc.vnet.net>
• 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[  ] = { -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 system. 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

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

Guofeng

--
Guofeng Zhang
PhD student
Dept. of Mathematical and Statistical Sciences
University of Alberta
Edmonton AB