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An efficient method for the discrete linear $L_{1}$ approximation problem

Author: Nabih N. Abdelmalek
Journal: Math. Comp. 29 (1975), 844-850
MSC: Primary 65D15; Secondary 90C10
MathSciNet review: 0378354
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Abstract: An improved dual simplex algorithm for the solution of the discrete linear ${L_1}$ approximation problem is described. In this algorithm certain intermediate iterations are skipped. This method is comparable with an improved simplex method due to Barrodale and Roberts, in both speed and number of iterations. It also has the advantage that in case of ill-conditioned problems, the basis matrix can lend itself to triangular factorization and can thus ensure a stable solution. Numerical results are given.

References [Enhancements On Off] (What's this?)

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Additional Information

Keywords: Discrete linear <IMG WIDTH="28" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img11.gif" ALT="${L_1}$"> approximation, overdetermined system of linear equations, linear programming, dual simplex algorithm
Article copyright: © Copyright 1975 American Mathematical Society