I am using the MKL's preconditioned FGMRES solver and I am trying to understand what exactly is the vector that FGMRES is asking to apply the preconditioner to. From the reference for the solver, Saad's Iterative methods for sparse linear systems, the left-preconditioned GMRES iteration (I'm assuming that FGMRES does left-preconditioning, please correct me if I'm wrong) involves computing at each step M^-1 A v_j. That is, FGMRES first asks to compute the matrix vector product A v_j, and then I would assume that FGMRES would ask to apply the preconditioner on that result, i.e. compute M^-1 A v_j. Only, when I compute the squared 2 norm of the vectors involved, I get that the vector on which FGMRES asks to apply the preconditioner (which I would assume to be A v_j) always has a unit norm, regardless of the norm of A v_j. What is this unit norm vector that FGMRES is asking the user to apply the preconditioner to?
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