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Re: [Axiom-developer] Re: Documentation of Axiom

From: root
Subject: Re: [Axiom-developer] Re: Documentation of Axiom
Date: Tue, 13 Dec 2005 17:31:06 -0500

> I know this is probably not something you've thought much about yet
> Tim, but are we planning to add any kind of "awareness" of accuracy
> limitations and error analysis to the numerical abilities of Axiom? 

Accuracy is somewhere on the list of things to discuss as is
the applicable range of values. Also on the list is the question
of where the algorithm applies (which quadrant, for instance).
The FORTRAN code is generally double precision floating point.
The code is highly optimized and obviously debugged thru use.

One of the things to think about is "infinite precision" versions
of the algorithm in an infinite real number setting. Axiom is
capable of computing with multi-digit values well beyond what
the hardware supports. However that does drag us into Kahan's
area and I fear to tread where the Wolf lives. :-) 

Another thing on the thought list is how to carry the accuracy
limitations and errors along in the computation. My gut feel is
that interval arithmetic and provisos would be perfect for this.

Like any analog computation (which I used to do on analog computers
back in the day) you get to the issue of scaling and automatic
scaling. Fortunately it doesn't involve rewiring :-)

There are lots of issue to cover in the documentation which, like
the units problem you are attacking, I have to learn in detail. If
I get it done in time I'll post the very first version of Volume 10
along with the next patch release.


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