Re: A problem of numerical precision

*To*: mathgroup at smc.vnet.net*Subject*: [mg52637] Re: A problem of numerical precision*From*: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>*Date*: Sun, 5 Dec 2004 02:08:18 -0500 (EST)*References*: <200412030815.DAA25377@smc.vnet.net> <cos0ps$dhq$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In version 5.1 (Windows XP) I get exactly the same result in both cases. Steve Luttrell "Guofeng Zhang" <guofengzhang at gmail.com> wrote in message news:cos0ps$dhq$1 at smc.vnet.net... > > 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 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 > point instead of wandering around! > > 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 > Canada T6G 2G1 > www.ece.ualberta.ca/~gfzhang >

**Follow-Ups**:**Re: Re: A problem of numerical precision***From:*DrBob <drbob@bigfoot.com>