Preconditioners for the resolution of the linear systems Ax=bAx=b

The aim of this work is to propose four preconditioners in order to resolve linear systems Ax=bAx=b, where A is a symmetric positive definite matrix. To do so, the iterative method of the preconditioned conjugate gradient is applied. The first three preconditioners are obtained from the quasi-newtonian method as an approximate inverse of the matrix A  . The fourth is an approximate inverse A∼-1 calculated by the algorithm (A∼I). This algorithm derives from (AIAI) proposed to compute the inverse of regular matrices.