Strict Discrete Approximation in the L 1 and L ∞ Norms

SUMMARY The L 1 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 L 2 solution from the convex set of all best L 1 or L ∞ solutions. Some numerical examples are presented and the stability of unique solutions is examined. The possibility and probability of non‐unique L 1 solutions for simple regression are discussed. A sufficient condition is obtained for data sets with equally spaced x i ,to have a unique L 1 line.