On the role of "professional developers" -
I think professionally developed libraries would be welcomed IF
1) They met the needs of the users. Numerical analysis just
doesn't seem to be viewed as a good marketing opportunity
by many companies. As a result the software that is needed
just isn't being written by the professionals, and the
amateurs (of which one I consider myself) are left with
the choice of nothing or doing it themselves. Are the
economics likely to change?
2) They work together. The professionals have a strong incentive
to short circuit the competition, so we tend to get products
that only function together within a tight bundle. Of course,
we amateurs don't plan anything on a grand scale (except things
like this mailing list, which is making an effort!), so
nothing seems to work together.
On the suggested decomposition -
Bravo! Numerical analysis is much more than linear algebra!
(Although LA important, and one of the few areas that seems
to be under control).
One thing that is left out from your decomposition are the
"things" (other than matrices) that these tools take as input
and output:
Geometrical regions and grids
Functions
Operators
Note that matrices are used in NA to represent many more things
than linear operators (like functions on regular grids), and I
think this distinction between the mathematical object and the
data structure must be more firmly made.
Mike Henderson http://www.research.ibm.com/nao
mhender@watson.ibm.com