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From: jurjen@cwi.nl (Jurjen NE Bos)
Newsgroups: comp.sys.handhelds
Subject: Re: The Solver
Message-ID: <1993@charon.cwi.nl>
Date: 23 Aug 90 08:20:36 GMT
References: <3346@rwthinf.UUCP>
Sender: news@cwi.nl
Lines: 34

berg@cip-s03.informatik.rwth-aachen.de (AKA Solitair) writes:

>Hello HP*8-hackers!  Here I have a somewhat "high-level" question.
>I don't know if this has been explained before, but does anybody have
>the details on how the solver exactly works?

>I mean what it exactly does with the initial guesses you give it, and
>how it extrapolates?  Maybe someone at HP could shed some light onto this?
>(It should not be that classified, I guess :-)
>--

The solver is an incredible complex program, and it works better and more
complicated than any equivalent program I have ever seen before.

I worked a little bit on figuring out what the solver does, and I found
the following:
It will use some tricks, that work about as stated below:
Normally (if there is a sign change), it does the well-known secant method.
If all three points have the same sign, take the the zero of the parabola
that goes through those points;
If this parabola does not have a zero, take the top;
If the middle point does have a high absolute value, take the zero of the
hyperbola through the three points;
If a point is undefined, take the average between this point and the previous
one;
(And sometimes it does something else that I don't understand).

As I recall, the programmer of this (wasn't that Bill Wickes Himself?) got
a prize for this formidable piece of numeric programming art.
--
|                 | "Never imagine yourself not to be otherwise than what |
| Jurjen N.E. Bos | it might appear to others that what you were or might |
|                 | have been was not otherwise than what you had been    |
|  jurjen@cwi.nl  | would have appeared to them to be otherwise."         |