Some feasible direction methods for the minimization of a linearly constrained convex function are studied. Special emphasis is placed on the analysis of the procedures which find the search direction, by developing active set methods which use orthogonal or Gauss-Jordan-like transformations. Numerical experiments are performed on a class of quadratic problems depending on two parameters, related to the conditioning of the matrix associated with the quadratic form and the matrix of active constraints at the optimal point. Results are given for the rate of convergence and the average iteration time.