--- Al Chou <[EMAIL PROTECTED]> wrote:
[deletia]--- Phil Steitz <[EMAIL PROTECTED]> wrote: [deletia]
OK, long-winded disclaimer aside, here is how I see the task list ordered:
* 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/ .
__________________________________ Do you Yahoo!? Yahoo! Calendar - Free online calendar with sync to Outlook(TM). http://calendar.yahoo.com
--------------------------------------------------------------------- To unsubscribe, e-mail: [EMAIL PROTECTED] For additional commands, e-mail: [EMAIL PROTECTED]
--------------------------------------------------------------------- To unsubscribe, e-mail: [EMAIL PROTECTED] For additional commands, e-mail: [EMAIL PROTECTED]
