Abstract
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. 
Highlights
L1 norm criterion is going to find its place in scientific analysis
The proposed algorithms are based on a special descent method and use a discrete differentiation technique
Primary designs of the algorithms have been discussed by Bidabad (1987a,b,88a,b)
Summary
L1 norm criterion is going to find its place in scientific analysis. Since it is not computationally comparable with other criteria such as L2 norm, it needs more work to make it a hand tool. Any attempt to give efficient computational algorithms which may introduce significant insight into the different characteristics of the problem is desirable In this regard, Bidabad (1989a,b) gives a general procedure to solve the L1 norm linear regression problem. For the second part of the computation, there is no special purpose procedure, but Bloomfield and Steiger (1980) used the partial sorting of Chambers (1971) to give an efficient way to combine the two steps of sorting and finding the optimal observation. The superiority of this procedure is in sorting the smaller segments of the array rather than all its elements.
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