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

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005558
URN to cite this document: urn:nbn:de:bvb:703-epub-5558-5

Title data

Baier, Robert:
Generalized Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis.
Bayreuth , 2006

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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.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): Erscheint in: Staicu, Vasile (Hrsg.): Differential Equations, Chaos and Variational Problems. - Basel : Birkhäuser , 2007 . - S. 49-60; https://doi.org/10.1007/978-3-7643-8482-1_4
Keywords: Generalized Steiner selections; Set-valued quadrature methods and interpolation; Linear differential inclusions; Attainable sets; Lipschitz and absolutely continuous selections; Set operation
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5558-5
Date Deposited: 19 May 2021 10:40
Last Modified: 17 Jun 2021 09:13
URI: https://epub.uni-bayreuth.de/id/eprint/5558

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