  In this article, we consider the primal-dual path-following method and the
trust-region updating strategy for the standard linear programming problem. For
the rank-deficient problem with the small noisy data, we also give the
preprocessing method based on the QR decomposition with column pivoting. Then,
we prove the global convergence of the new method when the initial point is
strictly primal-dual feasible. Finally, for some rank-deficient problems with
or without the small noisy data from the NETLIB collection, we compare it with
other two popular interior-point methods, i.e. the subroutine pathfollow.m and
the built-in subroutine linprog.m of the MATLAB environment. Numerical results
show that the new method is more robust than the other two methods for the
rank-deficient problem with the small noise data.
