🚀 go-pugleaf

In article <1993Jan8.201645.14915@news.eng.convex.com> dodson@convex.COM (Dave Dodson) writes:
>I'd like to point out that it is almost never required or desirable to
>compute the inverse of a matrix.  Almost without exception, you can do
>any computation in which you would use the inverse in a better way that
>does not use the inverse.  By 'better' I mean faster, uses less memory,
>more accurate, etc.

The direct use of the inverse matrix is generally the fastest way to
solve a dense system of equations with multiple, consecutive right-hand-sides
(as in a time-dependent fluid dynamics problem).

On the Cray Y series, for example, multiplying by the inverse matrix is
always (?) faster than performing the forward-backward substitution
step for each new RHS.  This is true even though both operations have
the same computational complexity in terms of operation counts (=2 N^2).
The difference is that matrix multiplication is a significantly
simpler algorithm with less overhead than forward-backward substitution.   

I suspect that the same sorts of speedups would be observed on Dodson's
Convex machines....
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John D. McCalpin                        mccalpin@perelandra.cms.udel.edu
Assistant Professor                     mccalpin@brahms.udel.edu
College of Marine Studies, U. Del.      John.McCalpin@mvs.udel.edu