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Approximation problems for convex polyhedra

Published online by Cambridge University Press:  26 February 2010

G. C. Shephard
G. C. Shephard
Affiliation:
Department of Pure Mathematics, The University, Birmingham.
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Let K be any convex body in En, and K any given class of convex sets in En. Then we shall say that K is approximable by the class K if there exists a sequence of sets {Ki}, such that, as i→∞, Ki→K in a suitable metric (for example, the Hausdorff metric), where each set Ki is a vector sum of (a finite number of) sets of the class K An approximation problem is to determine necessary and sufficient conditions for K to be approximable by a given class K.

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Type
Research Article
Information
Mathematika , Volume 11 , Issue 1 , June 1964 , pp. 9 - 18
Copyright
Copyright © University College London 1964

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References

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