I have the two following algorithms for GMRES(m) and left preconditioned GMRES.
I would like to know if anyone could explain why steps 10 through 12 are not used in the left preconditioned GMRES. Are they lost, or is it implicit that these need to happen?
If not, am I correct to assume that left-preconditioned works in blocks of m-vectors (number of vectors chosen before the restart of the Krylov subspace). So, if I choose 20 vectors to store before the restart, it will assemble all 20 Krylov subspace basis, and only afterward move to step 12?