Accuracy and error analysis (was Re: [Maxima] primes)

--- Albert Reiner  wrote:
> [Richard Fateman , Fri, 13 May 2005 13:01:44
> -0700]:
> > The reality is that most people do not do error analysis at all.
> > If they care, they run the same program but in higher precision
> > and see if it gets the same answer. If it doesn't, they run it
> > in higher-yet precision. Less human effort.
> 
> But now, it seems, you are only considering round-off errors, not the
> propagation of, say, measurement uncertainties.
> 
> Regards,
> 
> Albert.

Although my guess is for numerical calculations automating that process
will be both useful and generally sufficient - if a difference is
increasing with increasing precision that can and probably should
trigger an error, I suspect he might also be right in the larger case -
that very few people do really rigorous error analysis even when
measured uncertainties are involved - "reasonable" is generally enough
:-/.  Perhaps I'm wrong, but I would think that if I am a full semester
course or more entirely on error analysis would be mandatory for all
physical sciences, and ideally published as an appendix on all papers
reporting measured results (to prove that claims made are in fact
beyond the significant figures of the data in question.)  If Maxima
(and perhaps even more appropriately Axiom) were to make this job more
automated and straight forward (and I suspect for many much better
defined) than perhaps such analysis would become more common.

CY


		
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