Abstract
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.
 
Highlights
The objective of this paper is to compare some of the existing algorithms for the L1 norm regression with those proposed by Bidabad (1989a,b)
(1989a,b), many algorithms exist for L1 norm regression with corresponding computer program and comparison of all of them is very costly
Since in computational algorithms, accuracy is more important than efficiency, those L1 norm algorithms should be selected which produce correct solutions, and among them, the fastest one should be selected
Summary
The objective of this paper is to compare some of the existing algorithms for the L1 norm regression with those proposed by Bidabad (1989a,b). Our point of view is to compare the accuracy and relative efficiencies of them. In this respect, accuracy of the solution of the algorithms is more important than the other criteria. We mean that the algorithm performs with a smaller amount of required storage and execution time to reach the accurate optimal solution. The comparison of algorithms is not a straightforward task. As it is indicated by Dutter (1977), factors such as quality of computer codes and computing environment should be considered. Kennedy and Gentle and Sposito (1977a,b), and Hoffman and Shier (1980a,b) describe methods for generating random test data with known L1 norm solution vectors. Kennedy and Gentle and Sposito (1977a,b), and Hoffman and Shier (1980a,b) describe methods for generating random test data with known L1 norm solution vectors. Gilsinn et al (1977) discuss a general methodology for comparing the L1 norm algorithms. Kennedy and Gentle (1977) examine the rounding error of L1 norm regression and present two techniques for detecting inaccuracies of the computation (see Larson and Sameh (1980))
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