Algorithm for very fast computation of Least Absolute Value regression

The Least Squares (LS) problem has been popular in industrial modeling applications due to its speed, efficiency and simplicity. However, the LS solution is known to be unreliable when the data distribution is not Gaussian and is flat-tailed and such data anomalies occur frequently in the industry. The Least Absolute Value (LAV) problem overcomes these difficulties but at the expense of greatly increasing the complexity of the solution. This was partly addressed when it was shown that the LAV problem could be formulated as a Linear Programme (LP). However, the LP formulation is not suitable for implementation in all types of applications. In this paper, a very fast direct search algorithm is developed to solve the general dimension LAV problem using only elementary operations. The algorithm has been shown to be significantly faster than the LP approach through several experiments.