Abstract
Interior point methods specialized to the L 1 fitting problem are surveyed and the affine-scaling primal method is presented. Their main features are highlighted and improvements are proposed for polynomial fitting problems. For such problems, a careful handling of data avoids storing of matrices for the interior point approaches. Moreover, the computational complexity of iterations is reduced. An inexpensive way to compute a basic solution, using interpolation, is also provided. Extensive numerical experiments are carried out, including comparisons with a specialized simplex method. In general, the interior point methods performed better than the simplex approach. Among the interior point methods investigated, the dual affine scaling version was the most efficient.
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