Preconditioning in Conjugate Gradient

• This is a general technique, where one finds M such that can be easily solved and is numerically faster (easier or more stable) to solve than A

  i.e., M is an approximation to A whose inverse can be found easily---more precisely, for which linear equations can be solved as one never inverts matrices in this type of problem.

• The simplest preconditioner is M = Diagonal part of A.

• The best solution methods use sophisticated preconditioners such as those given by multigrid.