A nearest point algorithm for convex polyhedral cones and applications to positive linear approximation

Author:
Don R. Wilhelmsen

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

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose *K* is a convex polyhedral cone in and is defined in terms of some generating set . A procedure is devised so that, given any point , the nearest point *p* in *K* to *q* can be found as a positive linear sum of points from the generating set. The procedure requires at most finitely many linear steps.

The algorithm is then applied to find a positive representation

*L*acting on a suitable finite-dimensional function space .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1976-0394439-5

Keywords:
Convex set,
nearest point,
projection,
positive linear approximation,
linear algorithm,
cubature

Article copyright:
© Copyright 1976
American Mathematical Society