Re: Development of computer analysis systems
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 20 Mar 2008 13:59:57 -0400
In article <qGcEj.24098$R84.18062@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
Nasser Abbasi <nma@xxxxxxxxx> wrote:
"Herman Rubin" <hrubin@xxxxxxxxxxxxxxxxxxxx> wrote in message
news:frrdhn$1fj4@xxxxxxxxxxxxxxxxxxxxxxx
Symbolic computation is useful in numerical
computation, and that is very useful in graphics,
but the other way does not work well, but it is
of use. Computers are superfast subimbeciles,
and should be treated as such.
Agree that symbolic is useful (in numerical) work, but only for problems of
small size.
Disagree. Problems of fairly large size can profit from
it, and solutions to small size problems are often useful
in problems of large size.
One also has to use small size problems to debug for large
size.
For school project I wrote a small finite elements program, where I kept
everything in symbols, i.e. the stiffness matrix remained fully symbolic,
all the integration was kept symbolic, etc.., but it was too slowww, and for
anything more than few elements, it would take an hour or more on my PC and
would become short of memory fast (it was a one year old PC, not one of the
new multi-core Intel ones).
This I can well believe. For "production" runs, it is
generally better to find a way to use the smaller precision
computer hardware than to use a symbolic program at all.
I believe the main pacakges allow a Fortran or C compilation.
When I told Mathematica at the start to use numerics (for example, write
"10." instead of "10", and use NIntegrate instead of Integrate, etc...) the
finite elements program would run much much faster and what was taking one
hour would take less than a minute.
I have even had Mathematica make a major error by using
13 instead of 13. and 15 instead of 15.; it decided to
use an "exact" procedure, however using a packaged value
of an irrational with not enough accuracy. I did not
tell it to compute that way.
I think using CAS here was useful for me here to 'see things' better, but
when it comes to doing something in practice, it seemed to me it is still
too slow to use symbolic all the way for numerical work. May be the
multi-core CPU's coming out would help here?
Nasser
ps. I hope I understood what you meant by using symbolic in numerical
computation as meaning something as the above.
It is rare that I would use a CAS for a big numerical
calculation. I am quite aware that the way the symbolic
packages do arithmetic may even be worse than the way I
would do multiple precision arithmetic; I would not
bother with doing it decimally, but keep it all in hex.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.
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- From: Herman Rubin
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- From: Nasser Abbasi
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