Sum of Distances in Normed Spaces
Technical rept. Apr 90-Oct 90,
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
Pagination or Media Count:
A geometric proof for the following theorem due to Martelli and Busenberg is given. Integral geometry is used to discuss special cases and related results. Minkowski spaces are simply finite dimensional normed linear spaces. Smoothness assumptions on the boundary of the unit disk E for a Minkowski plane will enable us to use Croftons simplest formula from integral geometry to give a proof for three points. If the unit ball for a 3-dimensional Minkowski space is a zonoid, then we used integral geometry for the case of four points forming a simplex. A zonoid is a limit of sums of segments. Bolker discusses equivalent conditions for a convex subset of Rn to be a zonoid.
- Numerical Mathematics