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Speeding up calculations by lowering the precision ?

• To: mathgroup at smc.vnet.net
• Subject: [mg7913] Speeding up calculations by lowering the precision ?
• From: "Frank" <F.J.M.Geurts at fys.ruu.nl>
• Date: Mon, 21 Jul 1997 03:22:05 -0400
• Organization: Universiteit Utrecht
• Sender: owner-wri-mathgroup at wolfram.com

Hi,
I've written a lengthy math file which will eventually perform some
numerical calculations based on a couple of NIntegrate's. Right now, these
calculations take a very long time on a 466Mhz Alpha (running Math 2.2.4 /
Digital Unix 4.0). In fact i'be estimated another month (!). Everything
runs under 'default' conditions, i.e. Precision and WorkingPrecision are
based on the $MachinePrecision (which is 16). However, I am not really
interested in this high Precision but in high Speed : I would like all my
calculations to be performed at a 4-5 digit precision. I'm getting rather
confused of the actual Precision since after forcing NIntegrate with
WorkingPrecision->8 and PrecisionGoal->4 Mathematica still claims 16digit
precision in the results ...

Can anybody help me out on these two questions:
1) Can (extensive) calculations be speeded up by lowering the Precision
_below_ the $MachinePrecision ?
2) How can I be sure that all the calculations will be at a maximum 
precision set by me, without having to control/adjust each NIntegrate ?


best regards,
Frank

---
 F.J.M. Geurts        Dept. Subatomic Physics  Utrecht University
 R.J.v/d Graafflab.   +31-30-2532210/1492      geurts at fys.ruu.nl
 p.o. box 80,000      fax:   2518689      http://www.fys.ruu.nl/~geurts
 3508 TA  Utrecht     The Netherlands