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

Title data

Baier, Robert:
Generalized Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis.
In: Staicu, Vasile (ed.): Differential Equations, Chaos and Variational Problems. - Basel : Birkhäuser , 2007 . - pp. 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

Review:

Abstract in another language

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: Article in a book
Refereed: Yes
Additional notes: 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
Subject classification: Mathematics Subject Classification Code: 54C65 (93B03 93C05 28B20)
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 04 Mar 2021 09:47
Last Modified: 25 Mar 2021 06:04
URI: https://eref.uni-bayreuth.de/id/eprint/63666