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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.

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Publikationsform: Aufsatz in einem Buch
Begutachteter Beitrag: Ja
Zusätzliche Informationen: Contents:
1. Preliminaries
2. Representation and Arithmetics of Sets
3. Regularity of Set-Valued Maps
4. Set-Valued Interpolation and Quadrature Methods
5. Linear Differential Inclusions
6. Conclusions
Keywords: Generalized Steiner selections; Set-valued quadrature methods and interpolation; Linear differential inclusions; Attainable sets; Lipschitz and absolutely continuous selections; Set operation
Fachklassifikationen: Mathematics Subject Classification Code: 54C65 (93B03 93C05 28B20)
Institutionen der Universität: Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik
500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 04 Mär 2021 09:47
Letzte Änderung: 19 Mai 2021 10:41
URI: https://eref.uni-bayreuth.de/id/eprint/63666