In this paper, we consider the predictor-corrector method, which is one of the most important variants of the interior point methods due to its efficiency and fast convergence. In the predictor-corrector method it is necessary to solve two linear systems at each iteration to determine the search direction. The solution of such systems is the step that requires more processing time and should therefore be carried out efficiently. Two iterative Krylov methods are considered to solve these linear systems of: the MINRES and the conjugate gradient method. A preconditioner specially developed for the linear systems arising from the interior point methods is used so that the iterative methods converge faster. Computational experiments in a some sets of linear programming problems are performed in order to analyse the efficiency and robustness of the linear systems solution methods.
interior point methods; linear systems; iterative methods
