From reading in my text on this method they say that $P$ is the preconditioned matrix but they do not define it in any way shape or form. I am not sure at all, but by my professors psedo-code I would guess that $M$ is $P$? I honestly have no idea if that is the case. I have tried to search online for this but I seem to be getting information that is not very consistent with the way our book/professor presents the material.
Update: $M$ is just a general precondition matrix; i.e. Jabobi, or any other precondition matrix. The problem I seem to be having now is that I do not really understand the pseudo-code. I have all the ingredients necessary to start but I am not sure how to begin.
Note: the book I am using is, A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics,