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From "Phil Steitz" <p...@steitz.com>
Subject Re: [math] Greetings from a newcomer (but not to numerics)
Date Sun, 25 May 2003 15:43:01 GMT
Al Chou wrote:
> Greetings to the commons-math community!  I emailed Robert Donkin privately a
> few days ago asking, as I take it others have, about the reasoning behind
> creating a numerics library from scratch rather than incorporating an existing
> one.  I think I understand that reasoning now, but despite not wanting to
> dampen anyone's enthusiasm, I do want to caution those who have not done a lot
> of numerical computing that it can very easily be done wrong.

No question about that.  As I have stated a couple of times, however, I 
do not personally see commons-math as a numerics library.  There will 
certainly be numerical considerations to worry about, though, and your 
point is well taken.

  A big reason why
> there's a lot of legacy code in scientific computing is that it's hard to get
> numerical algorithms right, so once you do, there's great inertia towards
> changing anything (there are of course other big reasons, such as the fact that
> many computational scientists are not actually as computer-savvy as they are
> science-savvy, so they're not very facile at creating new code).
> 
Whence the wonderful proliferation of Fortran code in Java ;-)

> As an example, the high school quadratic formula 
> r = ( -b +- sqrt( b^2 - 4 * a * c ) ) / ( 2 * a )
> is extremely inaccurate, because of finite-precision arithmetic, when
> 4 * a * c << b^2 ,
> because of the subtraction of nearly-equal values.  But in high school they
> never teach you that fact.
> 
> On a more positive note, let me recommend _Numerical Recipes_, _Numerical
> Methods that [Usually] Work_ (which incidentally presents an alternate
> quadratic formula for use in the regime where the traditional one fails), and
> _Real Computing Made REAL_ as easy-to-read and down-to-earth references that
> show how easy it is for the naive implementation to be woefully inadequate as
> well as teach how to do numerical math correctly.

No question that the first of these at least and Knuth are classics to 
refer to. I am not familiar with the second two -- thanks for the tip. I 
also refer to Burden and Faires and Atkinson's _Numerical Analysis_ 
texts.  Do you know of any decent web numerical analysis references?  I 
have not been able to find much.  It would be nice to have some of these 
as well so we could refer to them in the docs and discussion.  In any 
case, it is probably a good idea to add a bibliography section to the 
web site.

> 
> I'd like to participate in commons-math in an advisory capacity of some sort,
> as I can't in good faith commit to being able to contribute code to the
> project.  Robert indicated that such a role would be useful to the project, so
> I hope you all feel the same!

Please, please, please!  Whatever time you have to review 
implementations, comment on strategies, and patiently point out our 
numerical blunders will be greatly appreciated.

Your frank assessment of project direction and the whole question of 
whether or not we should implement the things on the task list
(http://jakarta.apache.org/commons/sandbox/math/tasks.html) would also 
be appreciated.

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