Hyperplane Approximation and Related Topics

This chapter is a survey on problems related to the approximation of finite weighted point sets in d-space by hyperplanes with respect to certain metrics. From the viewpoint of Computational Geometry, we shall discuss the orthogonal and vertical L₁-fit problem as well as the orthogonal and vertical L_∞-fit problem. Though we shall lay emphasis on the othogonal L₁-fit problem, suitable generalizations to the other problems are given as well. For example, the reader will find informations on k- flats, k ∈ {0,…, d - 2}, being extremal with respect to finite point sets and leading also to the well-known Fermat-Torricelli point and related subjects.