L ₁ solution of overdetermined systems of linear equations

In a previous paper by the author, an algorithm for calculating the L1 solution of an overdetermined system of linear equations was given. This algorithm applies a dual simplex method to the linear programming formulation of the L1 approximation problem. For the purpose of numerical stability, the present paper uses a triangular decomposition to the basis matrix. This decomposition method is a new one and is particularly suitable to this algorithm. Numerical results show that the present method compares favorably with the best existing algorithms.