TY - JOUR
T1 - On the boundedness of an iteration involving points on the hypersphere
AU - Binder, Thomas
AU - Martinetz, Thomas
PY - 2012/12/1
Y1 - 2012/12/1
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.
UR - http://www.scopus.com/inward/record.url?scp=84876211093&partnerID=8YFLogxK
U2 - 10.1142/S0218195912500136
DO - 10.1142/S0218195912500136
M3 - Journal articles
AN - SCOPUS:84876211093
SN - 0218-1959
VL - 22
SP - 499
EP - 515
JO - International Journal of Computational Geometry and Applications
JF - International Journal of Computational Geometry and Applications
IS - 6
ER -
