A recursive algorithm for discrete L1 linear estimation using the dual simplex method

One of the practical problems in engineering and science is the estimation of parameters for given experimental data. It is also often required to update the estimates as new points are added to or as old points are deleted from the given data set. For data containing wild points, parameter estimation using approximation in the
L
₁
norm is usually recommended over other norms. It is shown that the updating of the estimates can be calculated with very little effort using parametric programming techniques applied to an existing
L
₁
approximation algorithm that itself uses a dual simplex method. Thus, an online adaptation for this algorithm is highly desirable. Numerical results and comments are given.