Richard Fateman wrote:
> Just looking at more of my notes, in
> http://www.cs.berkeley.edu/~fateman/generic/interval.tex, (which is the raw
> source tex and has lots of notes not in the pdf, notes-intervals.txt, and
> ninterval.lisp,
> I thought I might add some simple observations. e.g.
> evaluating a*x^2+b*x+c for numbers a,b,c and interval x, should not be done
> either by the "obvious" way, nor by Horner's rule: we use completing the
> square to make the evaluation use x a SINGLE time. transform
> a*x^2+b*x+c => a* (x^2+(b/a)*x* +c/a)
> (x^2+r*x +s) => (x + r/2)^2 -(r/2)^2 +s.
>
> why? you get a smaller interval for almost no extra work.
>
> This is much more interesting that implementing, for the hundredth time,
> interval versions of +,*, ... and trying to merge them in to maxima. What
> is infinity * interval? what if the interval is empty, e.g. the
> intersection of two distinct ranges? What are the rules for multiplying it
> by "und"?
>
> RJF
>
>
>
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>
>
Hello,
I have written a very minimal type of interval package in maxima which I
am attaching in case anyone wants to play with it.
It does no infinities, rounding, etc. It has no tricks.
It simply defines interval arithmetic operations for real valued
polynomials and rational functions in one or several variables in a more
or less obvious way.
So far, it gives (of course pessimistic) range enclosures for any
functions I have tried as long as I stay away from the boundaries of the
domain intervals. If there are bugs or suggestions about improvements,
etc, I would be very appreciative to know about them,
The short term goal for this package is to use rational arithmetic
whenever suitable for interval enclosures and subsume floating point
errors into intervals with rational endpoints.
I am a real novice in both programming and interval analysis, so I would
like to know about various kinds of tests or special polynomials or
rational functions one uses as test problems for these kinds of things.
FWIW,
-sen
I hope to try to exten
-------------- next part --------------
An embedded and charset-unspecified text was scrubbed...
Name: IN_1.mac
Url: http://www.math.utexas.edu/pipermail/maxima/attachments/20071216/21de2608/attachment-0001.diff