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Strict Discrete Approximation in the L 1 and L ∞ Norms
Author(s) -
Planitz M.,
Gates J.
Publication year - 1991
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347909
Subject(s) - mathematics , mathematical economics , physics
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.