Literatur vom gleichen Autor/der gleichen Autor*in
plus bei Google Scholar

Bibliografische Daten exportieren
 

Mengenwertige Integration und die diskrete Approximation erreichbarer Mengen

Titelangaben

Baier, Robert:
Mengenwertige Integration und die diskrete Approximation erreichbarer Mengen.
Bayreuth : Universität , 1995 . - XXII, 248 S. - (Bayreuther Mathematische Schriften ; 50 )

Rez.:

Abstract

This monograph is devoted to numerical integration of set-valued mappings. The approach chosen by the author is based on the following two facts: (1) the Aumann integral of a set-valued mapping F: [0,T] -> |Rn is a convex set and can be identified with its support function; (2) the value of the support function in any direction equals the integral of the support function of F in the same directions. For calculation of the latter integrals one can use any quadrature formula for (single-valued) functions. The accuracy of approximation depends on the chosen quadrature formula and on the ``smoothness" properties of the support function.
The realization of this approach and the corresponding error analysis are based on certain mathematical techniques that are comprehensively presented in the monograph: calculus with sets, elements of convex analysis (in particular, properties of the support function), moduli of smoothness, properties of the Aumann integral, and error estimates for classical quadrature formulae (Newton-Cotes, Gauss, Romberg, etc.).
The approach leads to a variety of set-valued quadrature formulae and corresponding error estimates. A separate chapter is devoted to numerical approximation of the reachable set of linear control systems, where error estimates are also obtained. Finally, possible computer implementations are discussed and a number of examples and computer plots are provided.
The monograph is clearly written, self-contained and could be useful for mathematicians interested in numerical analysis, control theory, set-valued analysis and differential inclusions.

Weitere Angaben

Publikationsform: Buch / Monografie
Keywords: Differentialinklusion; Diskrete Approximation; Integration <Mathematik>; Mengenwertige Abbildung; set-valued integration; reachable set; Aumann integral; Newton-Cotes formulas; Romberg integration; quadrature formulas; differential inclusion
Fachklassifikationen: Mathematics Subject Classification Code: 93B05 (49M25 65K10); 65D32 (26E25 28-02 28A78 28B20 41-02 41A55 41A65 65-02)
Institutionen der Universität: 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 > Ehemalige Professoren
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Fakultäten
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 29 Jan 2016 08:23
Letzte Änderung: 09 Apr 2021 06:48
URI: https://eref.uni-bayreuth.de/id/eprint/27418