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From: jwb@cepmax.ncsu.EDU (John W. Baugh Jr.)
Newsgroups: comp.specification
Subject: Re: Linear Algebra and Specifications
Message-ID: <1990Jul3.154807.20567@ncsuvx.ncsu.edu>
Date: 3 Jul 90 15:48:07 GMT
References: <9550@hubcap.clemson.edu> <1990Jun28.064022.13850@funet.fi> <1990Jun30.182211.25800@ncsuvx.ncsu.edu>
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I write about specifying matrix operators.

In article <9550@hubcap.clemson.edu>, steve@hubcap.clemson.edu ("Steve"
Stevenson) writes:
> As a numerical analyst with lots of interests and experience in numerical
> linear algebra, I think you're missing much of the point.
  [stuff deleted]
> There is no chasm between numerical analysis and linear algebra --- they're
> intimately intertwined.

Of course, I know that numerical analysis and linear algebra are
"intimately intertwined."  If you re-read my post you'll see that
I'm talking about _specifying_matrix_operators_.   My question
regards the level at which such operators are specified.  For
example, if I write a program that happens to make use of matrices,
I could take advantage of the "nice" algebraic properties of
real numbers, and hence the matrices defined over them, to reason
about my program.  Of course, matrices of finite-precision numbers
don't share these "nice" properties, which might encourage one to
specify even more details, namely a floating point representation
for matrix elements.  The trouble is that pretty soon I'm at an
"implementation" level, and I might just as well be writing
Fortran code (since I'm specifying all these details anyway).
The dramatic difference between these two levels of specification
is the "chasm" I'm referring to.  So, my question is: has any work
been done in the area of specifying matrix operators?

John Baugh
jwb@cepmax.ncsu.edu