Al Chou wrote:
> Greetings to the commonsmath 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 commonsmath 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 computersavvy as they are
> sciencesavvy, 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 finiteprecision arithmetic, when
> 4 * a * c << b^2 ,
> because of the subtraction of nearlyequal 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 easytoread and downtoearth 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 commonsmath 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
>
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