On 04/26/2018 10:16 AM, Bald Eagle wrote:
> William F Pokorny <ano### [at] anonymousorg> wrote:
> 
...
> 
> Just for clarification, POV-Ray uses:
> bisection
> regula falsa
> Newton's method, and
> the Sturmian method
> ?
> Or are some of those the same?
> 
> and - where is this all located in the source code?
> Because I'm a hopeless intellectual masochist like that.
> 

Thanks. Suppose I've been exposed to some of the concepts in the past, 
but trust me, I'm climbing the learning curve/mountain(a) with this 
stuff. There is much I don't understand. My standard set of test scenes 
number a 195 at present which have corrected many of my missteps.

You can find most of the code in source/core/math/polynomialsolver.cpp.

There are three custom solvers in solve_quadratic(), solve_cubic() and 
solve_quartic() for orders 2 through 4. I've hardly looked at these.

In polysolve / 'sturm' - a sturm chain based bisection method is used in 
combination with regula_falsa(). Value based bisection isn't used at 

in the sturm chain are, in my present version, the original and it's 
normalized derivative. Who knows, might play with it as an alternative 
or adjunct to regula_falsa(). The spin is it's really fast when it works 
- but sometimes it doesn't.

Near term looking more at the missing root issue - some(b) of which was 
addressed with (9), but the rest comes to the roots having collapsed 
toward each other so severely the sturm chain root counting / isolation 
falls apart. Not looking like it will be easy to mitigate...

Bill P.

(a) - Trying to get out of the media whirlpool! :-)

(b) - Where the sturm chain root counting and isolation stuff still 
works despite how close the roots are.

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