[petsc-users] Optimizing MatMatSolve

[Aron Ahmadia]

What Matt is getting at is that typically we measure the computational
difficulty of a problem as a function of the 'unknowns'.  If you are looking
at turning a sparse matrix O(n) bytes into a dense inverse O(n^2) bytes,
you've taken what was originally a potentially optimal problem and turned it
into one of quadratic difficulty in terms of memory, and even more in terms
of flops.  You may have better luck using an explicitly dense
method/algorithm for computing the inverse: it will scale well in the sense
that adding more processors will work faster (this is the heart of the
LINPACK computation after all), but you will need a lot of core-hours and
memory to get there...

A
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