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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A nearest point algorithm for convex polyhedral cones and applications to positive linear approximation
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by Don R. Wilhelmsen PDF
Math. Comp. 30 (1976), 48-57 Request permission

Abstract:

Suppose K is a convex polyhedral cone in ${E_n}$ and is defined in terms of some generating set $\{ {e_1},{e_2}, \ldots ,{e_N}\}$. A procedure is devised so that, given any point $q \in {E_n}$, the nearest point p in K to q can be found as a positive linear sum of ${N^\ast } \leqslant n$ points from the generating set. The procedure requires at most finitely many linear steps. The algorithm is then applied to find a positive representation \[ Lf = \sum \limits _{i = 1}^{{N^\ast }} {{\lambda _i}f({x_i}),} \quad {\lambda _i} > 0,f \in \Phi ,\] for a positive linear functional L acting on a suitable finite-dimensional function space $\Phi$.
References
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 48-57
  • MSC: Primary 52A25; Secondary 65D99
  • DOI: https://doi.org/10.1090/S0025-5718-1976-0394439-5
  • MathSciNet review: 0394439