This paper gives a rather general review of the L1 norm algorithms. The chronology and historical development of the L1 norm estimation theory for the period of 1632-1928 will be surveyed and the algorithms belonging to the after 1928 period will be categorized into three main classes of direct descent, simplex type, and other algorithms.

In this paper, the L1 norm of continuous functions and corresponding continuous estimation of regression parameters are defined. The continuous L1 norm estimation problem of one and two parameters linear models in the continuous case is solved. We proceed to use the functional form and parameters of the probability distribution function of income to exactly determine the L1 norm approximation of the corresponding Lorenz curve of the statistical population under consideration.

In this paper, three algorithms for weighted median, simple linear, and multiple m parameters L1 norm regressions are introduced. The corresponding computer programs are also included.

In this paper, we propose four algorithms for L 1 norm computation of regression parameters, where two of them are more efficient for simple and multiple regression models. However, we start with restricted simple linear regression and correspo nding derivation and computation of the weighted median prob lem. In this respect, a computing function is coded. With discussion on the m parameters model, we continue to expand the algorithm to include unrestricted simple linear regression, and two crud e and efficient algorithms are proposed. The procedures are t hen generalized to the m parameters model by presenting two new algorithms, where the algorithm 4 is selected as more efficient. Various properties of these algorithms are discussed.

This paper tries to compare more accurate and efficient L1 norm regression algorithms. Other comparative studies are mentioned, and their conclusions are discussed. Many experiments have been performed to evaluate the comparative efficiency and accuracy of the selected algorithms.