Sometimes when solving very sparse equation systems
with conjugate gradient using computers, if A is a very sparse matrix, it can be difficult to utilize the hardware computational power maximally
Does there exist some way to rewrite
to be able to utilize hardware better?
One idea I had is that often et.c. are increasingly non-sparse. Maybe it would be possible to take multiple steps at once..?
One motivation why this should be possible is that the Krylov subspaces which the Conjugate Gradient investigates are precisely the powers of the matrix. A second motivation why this is possible is of course Caley Hamilton theorem
For some polynomial other than P.