On the boundedness of an iteration involving points on the hypersphere

Thomas Binder; Thomas Martinetz

doi:10.1142/S0218195912500136

On the boundedness of an iteration involving points on the hypersphere

Institute of Neuro- and Bioinformatics

Abstract

For a finite set of points X on the unit hypersphere indwe consider the iteration ui+1 = ui+ χi, where χiis the point of X farthest from ui. Restricting to the case where the origin is contained in the convex hull of X we study the maximal length of ui. We give sharp upper bounds for the length of uiindependently of X. Precisely, this upper bound is infinity for d ≥ 3 and $\sqrt{2}$ for d = 2. © 2012 World Scientific Publishing Company.

Original language	English
Journal	International Journal of Computational Geometry and Applications
Volume	22
Issue number	6
Pages (from-to)	499-515
Number of pages	17
ISSN	0218-1959
DOIs	https://doi.org/10.1142/S0218195912500136
Publication status	Published - 01.12.2012

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SDG 9 Industry, Innovation, and Infrastructure

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abstract = "For a finite set of points X on the unit hypersphere indwe consider the iteration ui+1 = ui+ χi, where χiis the point of X farthest from ui. Restricting to the case where the origin is contained in the convex hull of X we study the maximal length of ui. We give sharp upper bounds for the length of uiindependently of X. Precisely, this upper bound is infinity for d ≥ 3 and \$\textbackslash{}sqrt\{2\}\$ for d = 2. {\textcopyright} 2012 World Scientific Publishing Company.",

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AU - Martinetz, Thomas

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N2 - For a finite set of points X on the unit hypersphere indwe consider the iteration ui+1 = ui+ χi, where χiis the point of X farthest from ui. Restricting to the case where the origin is contained in the convex hull of X we study the maximal length of ui. We give sharp upper bounds for the length of uiindependently of X. Precisely, this upper bound is infinity for d ≥ 3 and $\sqrt{2}$ for d = 2. © 2012 World Scientific Publishing Company.

AB - For a finite set of points X on the unit hypersphere indwe consider the iteration ui+1 = ui+ χi, where χiis the point of X farthest from ui. Restricting to the case where the origin is contained in the convex hull of X we study the maximal length of ui. We give sharp upper bounds for the length of uiindependently of X. Precisely, this upper bound is infinity for d ≥ 3 and $\sqrt{2}$ for d = 2. © 2012 World Scientific Publishing Company.

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JO - International Journal of Computational Geometry and Applications

JF - International Journal of Computational Geometry and Applications

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ER -

On the boundedness of an iteration involving points on the hypersphere

Abstract

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