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The Computer Journal 1973 16(2):180-186; doi:10.1093/comjnl/16.2.180
© 1973 by British Computer Society
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Discrete approximation in the L1 norm

K. Spyropoulos *, E. Kiountouzis * and A. Young *

School of Physical Sciences, (Mathematics), The New University of Ulster, Coleraine, UK

We present some theoretical results of the discrete approximation problem in the L1 norm based on the algebraic properties of a linear programming formulation. In particular we give a condition for uniqueness of the best approximation and a characterisation theorem which does not invoke the Haar condition. We show how a median property can be used to secure a much improved rate of convergence of linear programming solutions. We give an algorithm for fitting by general functions and a particularly fast algorithm using minimum storage requirements when fitting by polynomials.

Received April 1972.

* School of Physical Sciences, (Mathematics), The New University of Ulster, Coleraine, County Londonderry, Northern Ireland


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