> My reasoning is this. There often really _is_ a "best" algorithm to
> solve a particular problem. For example, no one solves very large,
> sparse, symmetric positive definite systems of equations using any
> algorithm other than conjugate gradient...
Ouch. I guess it's my turn to say this statement is way too strong.
Don't get me wrong: I'm a fan of iterative methods (after all, I co-authored
a book on this and developed IML++), but many of the finite-element
applications (which give rise to your SPD system) do _not _ use CG (or any
other iterative method, for that manner) but direct solvers on unassembled or
skyline storage matrices (which, by the way, _aren't_ MSR or Yale.) In numerical
computing, there is hardly ever a "best" algorithm for practically anthing ---
everything
is a subtle tradeoff. What's the best linear solver for sparse unsymmetric
systems?
Best preconditioner? Best non-linear, constrained optimization algorithm?
Best PDE solver? (Gulp.)
You don't really mean this, do you?
--Roldan