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
>>> www.ece.ualberta.ca/~gfzhang
>>>
>>
>>
>>
>>
>>
>
>
>
> --
> DrBob at bigfoot.com
> www.eclecticdreams.net
>

```

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