The rate of convergence of explicit approximate inverse preconditioning

Abstract

The rate of convergence of the explicit preconditioned methods, based on approximate inverses, is shown to be based on lower and upper bounds of the extreme eigenvalues of the iteration matrix. Estimates of the computational work required to reduce the Lr-norm by a factor e are given. The application of the method on a 2D elliptic boundary value problem is discussed and numerical results are given.