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From "Phil Steitz" <>
Subject Re: [math] proposed ordering for task list, scope of initial release
Date Sat, 07 Jun 2003 20:57:12 GMT
Al Chou wrote:


>>* Improve numerical accuracy of Univariate and BivariateRegression
>>computations. Encapsulate basic double[] |-> double mean, variance, min, max
>>computations using improved formulas and add these to MathUtils. (probably
>>should add float[], int[], long[] versions as well.) Then refactor all
>>univariate implementations that use stored values (including UnivariateImpl
>>with finite window) to use the improved versions. -- Mark?  I am chasing down
>>the TAS reference to document the source of the _NR_ formula, which I will
>>to the docs if someone else does the implementation.
> I was starting to code the updating (storage-less) variance formula, based on
> the Stanford article you cited, as a patch.  I believe the storage-using
> corrected two-pass algorithm is pretty trivial to code once we feel we're on
> solid ground with the reference to cite.  

Yes.  I just wanted to propose the refactoring.

>>* Framework and implementation strategie(s) for finding roots or real-valued
>>functions of one (real) variable.  Here again -- largely done.  I would
>>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?

I doubt that J would mind if someone else were to submit the framework 
(including his @author of course) from his post to the list.  You could 
combine his classes and yours into one patch and submit it if you have 
time to do this before he gets back.

>>* Polynomial Interpolation -- let Al tell us what to do here.  Even better,
>>let Al do it (he he).   
> I actually did some research last night (I told myself I was going to bed
> early, hah) on rational function interpolation, trying to find a primary source
> for the algorithm rather than again rely on a secondary source in the form of
> NR.  I guess I'll continue along this path, as I really want a clean room
> implementation of it for my own use.  I'd feel better using rational functions
> rather than polynomials for their generally larger radius of convergence.

Thanks for looking into this.  If you think rational functions are 
better, go for it.  One more thing to think about is splines. A natural 
spline implementation might be easier to document/understand from users' 
perspective. We might want to eventually support both (and maybe even 
polynomial interpolation).


> Al
> =====
> Albert Davidson Chou
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