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From "Phil Steitz" <p...@steitz.com>
Subject Re: [math] proposed ordering for task list, scope of initial release
Date Tue, 10 Jun 2003 13:46:43 GMT
Al Chou wrote:
> --- Al Chou <hotfusionman@yahoo.com> wrote:
> 
>>--- Phil Steitz <steitzp@yahoo.com> wrote:
>>[deletia]
>>
>>>OK, long-winded disclaimer aside, here is how I see the task list ordered:
>>
> [deletia]
> 
>>>* Framework and implementation strategie(s) for finding roots or
>>
>>real-valued
>>
>>>functions of one (real) variable.  Here again -- largely done.  I would
>>>prefer
>>>to wait until J gets back and let him submit his framework and R. Brent's
>>>algorithm.  Then "our" Brent's implementation and usage can be integrated
>>>(actually not much to do, from the looks of the current code) and I will
>>
>>add
>>
>>>my "bean equations" stuff (in progress).
>>
>>I may have time to submit my Ridders' method implementation using J.'s
>>framework before he returns 2 days hence.  Should I bother to try, or should
>>I
>>wait until he submits his code as a patch via Bugzilla?
> 
> 
> Well, I've just spent some time over the past 3 days reminding myself pf some
> of the things that are so hard about numerics.
> 

> BTW, in the process of using Herr Pietschmann's root finder framework, I
> discovered a bug in setMaximalIterationCount (it sets
> defaultMaximalIterationCount instead of maximalIterationCount).
>
> 
> So I pulled out Herr Pietschmann's Brent method class and tested it, and it
> threw an exception telling me, "Possibly multiple zeros in interval or ill
> conditioned function."
> 
> The morals of the story are:
>  - More-sophisticated algorithms that are supposed to converge faster don't
> always do so
>  - It's easy to outsmart yourself and create code that's too finicky for
> non-numericist users.

Good thing to keep reminding ourselves.

> 
> As someone said recently on the list, a typical user probably is more
> interested in an algorithm that's guaranteed to converge to a root (if there is
> one) than in the rate of convergence, as long as it's not too ridiculously
> slow.  Given that we've repeatedly determined that commons-math is not to be a
> general numerical mathematics library, I think now that we should provide only
> a bisection method in the initial release (assuming we achieve one) and spend
> time later making our implementations of the more sophisticated algorithms more
> user-friendly, if we find they're even needed.  

+1, but maybe adding Secant method (I think J included this as well, if 
memory serves).


> 
> Finally, having used the Pietschmann root finder framework, I think it needs
> some modification to make it more user-friendly.  As a lay user, I would have
> been much happier dealing with Brent W.'s interface than Herr Pietschmann's,
> which was kind of cumbersome.  I think, though, with a little slimming down, it
> would be quite workable.
> 

We should let J comment on this.  Also, the "bean equations" stuff that 
I am working on will be *very* easy to use (though less sophisticated).

> 
> Al
> 
> =====
> Albert Davidson Chou
> 
>     Get answers to Mac questions at http://www.Mac-Mgrs.org/ .
> 
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