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There are no matrix multiplications in linear solvers in general. There are Matrix vector multiplications, typically far fewer than the size of the matrix. This
by midjji 6y ago
There are no matrix multiplications in linear solvers in general. There are Matrix vector multiplications, typically far fewer than the size of the matrix. This confusion hides that solving linear systems was already far faster than matrixmatrix multiplication, and makes it seem like a stronger result than it is. I would like to see this compared to e.g. sparse cg, for any non random datamatrix.
- thomasahle 6y agoThis is a theoretical result - for now at least. Theoretically the fastest linear solvers run in time n^w where w ~ 2.3 is the matrix multiplication constant. In practice the fast matrix multiplication algorithms are not that fast, so they aren't used for linear solvers.