Re: Re: A problem of numerical precision

*To*: mathgroup at smc.vnet.net*Subject*: [mg52686] Re: Re: A problem of numerical precision*From*: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>*Date*: Thu, 9 Dec 2004 20:22:42 -0500 (EST)*References*: <200412030815.DAA25377@smc.vnet.net> <cos0ps$dhq$1@smc.vnet.net> <200412050708.CAA26762@smc.vnet.net> <cp3s6c$93p$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

You are correct; I just ran the code again and got the results you describe. I don't know what I did wrong the first time round to make the results come out the way they did for me. Steve Luttrell "DrBob" <drbob at bigfoot.com> wrote in message news:cp3s6c$93p$1 at smc.vnet.net... > I'm using 5.1 and got very different answers. Here's the second case: > > delta = 1/100; > a = 9/10; > b = -3*1.4142135623730950``200/10; > A = {{1, 0}, {b, a}}; > B = {{-1, 1}, {-b, b}}; > > f[v_, x_] := If[Abs[(10^20)*v - (10^20)*x] > (10^20)*delta, 1, 0]; > > M = 3000; > it = Table[0, {i, M}, {j, 2}]; > it[[1]] = {-delta/2, (a + b)*(-delta/2)}; > > For[i = 1, i < M, it[[i + 1]] = A.it[[i]] + > f[it[[i, 1]], it[[i, 2]]]*B.it[[i]]; i++]; > temp = Take[it, -1000]; > ListPlot[temp]; > > (a single point, where the other plot was a starburst) > > You do get the same result for both if you do this the second time: > > b = -3*1.4142135623730950``200/10; > M = 3000; > it = Table[0, {i, M}, {j, 2}]; > it[[1]] = {-delta/2, (a + b)*(-delta/2)}; > > For[i = 1, i < M, it[[i + 1]] = A.it[[i]] + f[it[[i, > 1]], it[[i, 2]]]*B.it[[i]]; i++]; > temp = Take[it, -1000]; > ListPlot[temp]; > > A and B didn't get reset, so it's a very different series. > > Bobby > > On Sun, 5 Dec 2004 02:08:18 -0500 (EST), Steve Luttrell > <steve_usenet at _removemefirst_luttrell.org.uk> wrote: > >> In version 5.1 (Windows XP) I get exactly the same result in both cases. >> >> Steve Luttrell >> >> "Guofeng Zhang" <guofengzhang at gmail.com> wrote in message >> news:cos0ps$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 >>> >> >> >> >> >> > > > > -- > DrBob at bigfoot.com > www.eclecticdreams.net >

**References**:**Re: A problem of numerical precision***From:*"Steve Luttrell" <steve_usenet@_removemefirst_luttrell.org.uk>