Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

Mengenwertige Integration und die diskrete Approximation erreichbarer Mengen

Title data

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

Review:

Abstract in another language

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.

Further data

Item Type: Book / Monograph
Keywords: Differentialinklusion; Diskrete Approximation; Integration <Mathematik>; Mengenwertige Abbildung; set-valued integration; reachable set; Aumann integral; Newton-Cotes formulas; Romberg integration; quadrature formulas; differential inclusion
Subject classification: Mathematics Subject Classification Code: 93B05 (49M25 65K10); 65D32 (26E25 28-02 28A78 28B20 41-02 41A55 41A65 65-02)
Institutions of the University: 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 > Former Professors
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 29 Jan 2016 08:23
Last Modified: 09 Apr 2021 06:48
URI: https://eref.uni-bayreuth.de/id/eprint/27418