Conjugate gradient type methods and preconditioning

摘要

In this paper we consider various iterative methods for the numerical solution of very large, sparse linear systems of equations, which arise in the discretization of partial differential equations. As the performance of the methods generally depends on the characteristics of the problems to be solved, a judicious choice between the methods will require knowledge about the system. The aim of this paper is to review the properties of the various iteration methods, in order to assist the user in making a deliberate selection.