The numerical software users are often perturbed by accuracy problems imputable to the rounding errors generated by computer hardware. M. La Porte and J. Vignes (4) created the permutation-perturbation method for evaluating the validity of the solutions of linear algebraic systems, detection of the matrix singularity, and optimal termination criterion of iteratives methods. These problems exist and are considerably amplified in linear and non-linear programming algorithms using near simplex methods : Reduced Gradient of P. Wolfe and Generalized Reduced Gradient of J. Abadie (1) ; effectively, these methods proceed with a long sequence of matrix inversions which increases rounding errors, and it is not unu4sual to obtain false basic solutions or singular basic matrices. Moreover, the classical termination criterions of unconstrained optimization may involve either an untimely stop of the algorithm producing a solution far from the optimum, or, on the contrary, a large number of unprofitable iterations which does not improve the current solution. I suggest, in this paper, some quick and efficient procedures for solving these problems.