Admittedly, I'm new to the subject, so this is probably a really simple question.
Let's assume I want to solve the (large sparse) linear system Ax = b multiple times with algebraic multigrid and b changes (slightly) every time. As I understand it, AMG selects its coarse grid based on the smoothness of the error, which depends on b, so this would have to be done anew every time b changes, although A stays the same.
Is this correct? And isn't this a huge bargain compared to geometric multigrid (when applicable)?