ISSN:
1572-9168
Keywords:
center hyperplane
;
centred hyperplane
;
distance
;
k-set problem
;
median hyperplane
;
Minkowski space
;
minsum hyperplane
;
norm
;
numerical approximation
;
point set width problem
;
robust statistics
;
smooth norm.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In an arbitrary Minkowski space M, n≥2, let there be given an arbitrary finite set P of weighted points whose affine hull is n-dimensional. We show that the unit ball B of M has smooth boundary if and only if each median hyperplane (minimizing the sum of weighted distances with respect to P) is spanned by n affinely independent points from P. Moreover, B has the same property if and only if every center hyperplane (minimizing the maximal weighted distance with respect to P) has the same maximal distance to at least n+1 affinely independent points from P.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1005165709146
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