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Re: For loop problem in mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg90188] Re: [mg90163] For loop problem in mathematica
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Wed, 2 Jul 2008 05:27:16 -0400 (EDT)
• References: <200807011059.GAA14895@smc.vnet.net>

On Jul 1, 2008, at 6:59 AM, PhysNova wrote:

> Hi,
> i wrote a simple program of evaluating Pi number in M6 to test cpu
> computation timing, to do this a simple for loop
>
> was used:
>
> x=0;For[i = 1, i < 10,000,000, i++, x = x + 1/(i^2)];N[Sqrt(6*x),25]//
> Timing
>
> the result was catastrophe! it take few minuates. but i first expect
> to do this very simple job in few
>
> seconds.computation time is just satisfactory up to 100000 cycle.
>
> could anyone interperet this falut?

You are using exact arithmetic, Mathematica will constantly try to  
preserve precision, and simplify the expression x + 1/i^2 which adds  
computational complexity.

> our get an idea to improve the result?

If you don't care about exact results, use approximate numbers:

x=N[0,25];For[i = 1, i < 10,000,000, i++, x =N[ x + 1/(i^2),25]];N 
[Sqrt(6*x),25]//
Timing

Regards,

Ssezi

• References:
  • For loop problem in mathematica
    • From: PhysNova <skhoshbinfar@gmail.com>