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From Al Chou <>
Subject Re: Update: [math] proposed ordering for task list, scope of initial release
Date Sun, 15 Jun 2003 14:15:10 GMT
--- Phil Steitz <> wrote:
> Here is an updated version.  I will try to submit a patch to the 
> task.xml reflecting this before I leave this AM, but I am running out of 
> time...

> > * Improve numerical accuracy of Univariate and BivariateRegression
> statistical
> > 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 (done), which
> I will add
> > to the docs if someone else does the implementation
> Al submitted a patch covering part of this last night.

Note that I didn't do anything in the finite-window part of
UnivariateImpl.insertValue(), because I didn't know how.  I just realized we
may just be able to use the "weight = -1" case described in Hanson and Chan &
Lewis.  I'll read them more carefully to see if that's correct.

Also, the corrected two-pass algorithm still needs to be put into
StoreUnivariateImpl, right?

> > * 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)
> Need to make a decision here.  I suggest that Brent makes the 
> improvements that he has in mind to J's framework, puts into the new 
> package (earlier post) and refactors existing stuff.

Sounds reasonable (or do I say "+1"?).  I think we need _something_ submitted
in the way of root finding framework so we can give feedback.

> > * Polynomial Interpolation -- let Al tell us what to do here.  Even better,
> let
> > Al do it (he he).  
> Use rational functions, per Al's suggestions.  Maybe implement natural 
> spline instead. Al? Anyone?

I need to find a non-NR reference to the Stoer and Bulirsch algorithm for
rational function interpolation (I don't own a copy of their book), otherwise
I'll just be relying on NR's description.

I don't have an objection to providing cubic splines, though we should be aware
that they open the door to providing a tridiagonal linear system solver.


Albert Davidson Chou

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