Abstract
Generalized Steiner points and the corresponding selections for setvalued 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.
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Dedicated to Arrigo Cellina and James Yorke
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Baier, R. (2007). Generalized Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis. In: Staicu, V. (eds) Differential Equations, Chaos and Variational Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 75. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8482-1_4
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DOI: https://doi.org/10.1007/978-3-7643-8482-1_4
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