In many applications, for many reasons, we have a starting guess of the solution. You might worry that you could not find the starting preconditioned variable because you did not know the inverse of . The way to avoid this problem is to reformulate the problem in terms of a new variable where . Then becomes or Thus we have accomplished the goal of taking a problem with a nonzero starting model and converting it a problem of the same type with a zero starting model. Thus we do not need the inverse of because the iteration starts from so .