On the boundedness of an iteration involving points on the hypersphere

Thomas Binder, Thomas Martinetz

For a finite set of points $X$ on the unit hypersphere in ${\mathbb{R}}^d$ we consider the iteration $u_{i+1}=u_i+{\chi }_i$, where ${\chi }_i$ is the point of $X$ farthest from $u_i$. Restricti…