  A class of interior point methods using inexact directions is analysed. The
linear system arising in interior point methods for linear programming is
reformulated such that the solution is less sensitive to perturbations in the
right-hand side. For the new system an implementable condition is formulated
that controls the relative error in the solution. Based on this condition, a
feasible and an infeasible potential reduction method are described which
retain the convergence and complexity bounds known for exact directions.
