Strict Discrete Approximation in the L1 and L∞ Norms

M. Planitz and J. Gates

Journal of the Royal Statistical Society Series C, 1991, vol. 40, issue 1, 113-122

Abstract: The L1 and L∞ solutions of an overdetermined system of linear equations are not necessarily unique. Assuming that the coefficient matrix has full column rank, a quadratic programming method is used to select the unique best L2 solution from the convex set of all best L1 or L∞ solutions. Some numerical examples are presented and the stability of unique solutions is examined. The possibility and probability of non‐unique L1 solutions for simple regression are discussed. A sufficient condition is obtained for data sets with equally spaced xi,to have a unique L1 line.

Date: 1991
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