Improving the preconditioning of linear systems from interior point methods

Abstract

This paper deals with preconditioners for solving linear systems arising from interior point methods, using iterative methods. The main focus is the development of a set of results that allows a more efficient computation of the splitting preconditioner. During the interior point methods iterations, the linear system matrix becomes ill conditioned, leading to numerical difficulties to find a solution, even with iterative methods. Therefore, the choice of an effective preconditioner is essential for the success of the approach. The paper proposes a new ordering for a splitting preconditioner, taking advantage of the sparse structure of the original matrix. A formal demonstration shows that performing this new ordering the preconditioned matrix condition number is limited; numerical experiments reinforce the theoretical results. Case studies show that the proposed idea has better sparsity features than the original version of the splitting preconditioner and that it is competitive regarding the computational time.