By use of multigrid method, this paper proposes a preconditioned iteration method solving the boundary value problem of elliptic equations, the proof of convergence is given.

Efficient multistep procedure for time-stepping Galerkin methods is derived and analyzed, in which used an alternating direction preconditioned iterative methods for approximately solving the linear equations arising at each timestep in a discrete Galerkin method for a class of linear parabolic systems.

Focusing on the problem that the extrinsic information transfer(EXIT) functions of the iterative processing unit in existing methods are of low accuracy,an accurate method named optimal histogram(OptHIST) is proposed.