On orthogonal linear approximation
Numerische Mathematik
Robust regression and outlier detection
Robust regression and outlier detection
Orthogonal weighted linear L1 and L∞ approximation and applications
Discrete Applied Mathematics
On bisectors for different distance functions
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Median hyperplanes in normed spaces — a survey
Discrete Applied Mathematics
Median and center hyperplanes in Minkowski spaces — a unified approach
Discrete Mathematics
On the circle closest to a set of points
Computers and Operations Research - Location analysis
Locating a minisum circle in the plane
Discrete Applied Mathematics
Median spheres: theory, algorithms, applications
Numerische Mathematik
Geometric fit of a point set by generalized circles
Journal of Global Optimization
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We study the minsum hypersphere problem in finite dimensional real Banach spaces: given a finite set D of (positively weighted) points in an n-dimensional normed space (n=2), find a minsum hypersphere, i.e., a homothet of the unit sphere of this space that minimizes the sum of (weighted) distances between the hypersphere and the points of D. We show existence results of the following type: there are situations where minsum hyperspheres do not exist, no point-shaped hypersphere can be optimal, and for any norm there exists a set of points D such that a hyperplane is better than any proper hypersphere. We also prove that the intersection of a minsum hypersphere S and conv(D) is non-empty, that D@?conv(S) implies |S@?conv(D)|=2, and that |S@?conv(D)|