This work presents two preconditioned versions of the conjugate gradient method. These versions differ from the classic version; they consider the linear system in form of normal equations. It will solve linear systems that arise from search directions computation in an interior point method. Determining the direction is the step with the largest computational effort and in large scale problems the use of direct methods might not be feasible. Therefore, one option is to use preconditioned iterative methods to solve the systems. The performances of these two versions of the preconditioned conjugate gradient methods are compared with the classic version. Numerical result shows that one of these versions is competitive with the classic one.
linear programming; interior point method; conjugate gradient
