Big float Round off errors



I am getting apoplexy.




 ------------Original Message------------
From: Barton Willis <willisb at unk.edu>
To: fateman at cs.berkeley.edu
Cc: "'Maxima List'" <maxima at math.utexas.edu>
Date: Wed, May-7-2008 4:09 PM
Subject: Re: [Maxima] Big float Round off errors

Thanks for this reference; some readers might enjoy the experiment:

 (%i33) fpprec : 20$
 (%i34) l : makelist((-75)^k/k!,k,0,500)$

 (%i35) bfloat(tree_reduce("+", map(lambda([s],
 rationalize(bfloat(s))),l)));
 (%o35) -5.3399030854116552833b10

 (%i36) bfloat(tree_reduce("+", l));
 (%o36) 2.6786369618080779443b-33

The reason (%o35) and (%o36) aren't close isn't subtractive
cancellation--the sum was done using rational arithmetic. The
problem is that the sum is ill-conditioned.

Barton

-----maxima-bounces at math.utexas.edu wrote: -----


>There is a brief summary of some of the many proposed ways of accurate
>summation here:
>
>http://hpcrd.lbl.gov/SCG/ocean/NRS/ECMWF/img11.htm
>
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