An Improved Algorithm for Discrete $l_1 $ Linear Approximation

TLDR: By modifying the simplex method of linear programming, this work is able to present an algorithm for l_1-approximation which appears to, be superior computationally to any other known algorithm for this problem.

Abstract: Work sponsored by the United States Army under Contract No.: DA-31-124-ARO-D-462. Department of Mathematics, University of Victoria, Victoria, B.C., Canada.

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Citation for this paper:
Barrodale, I. & Roberts, F.D.K. (1972). An Improved Algorithm for Discrete L1
Linear Approximation. MRC Technical Summary Report #1172.
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An Improved Algorithm for Discrete L1 Linear Approximation
Ian Barrodale and F.D.K. Roberts
MRC Technical Summary Report #1172
January 1972
A revised version of this internal report was later published in Society for Industrial
and Applied Mathematics (SIAM) Journal on Numerical Analysis:
October 1973, 10(5), 839–848.
https://epubs.siam.org/doi/abs/10.1137/0710069
and its Fortran Subroutine was later published in Communications of the ACM, as
Algorithm 478:
June 1974, 17(6), 319-320.
https://doi.org/10.1145/355616.361024