Generalized Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis

Titelangaben

Baier, Robert:
Generalized Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis.
In: Staicu, Vasile (Hrsg.): Differential Equations, Chaos and Variational Problems. - Basel : Birkhäuser , 2007 . - S. 49-60 . - (Progress in Nonlinear Differential Equations and Their Applications ; 75 )
ISBN 978-3-7643-8481-4
DOI: https://doi.org/10.1007/978-3-7643-8482-1_4

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Abstract

Generalized Steiner points and the corresponding selections for set-valued maps share interesting commutation properties with set operations which make them suitable for the set-valued numerical problems presented here. This short overview will present first applications of these selections to standard problems in this area, namely representation of convex, compact sets in |Rn and set operations, set-valued integration and interpolation as well as the calculation of attainable sets of linear differential inclusions. Hereby, the convergence results are given uniformly for a dense countable representation of generalized Steiner points/selections. To achieve this aim, stronger conditions on the set-valued map F have to be taken into account, e.g. the Lipschitz condition on F has to be satisfied for the Demyanov distance instead of the Hausdorff distance. To establish an overview on several applications, not the strongest available results are formulated in this article.