at Google ScholarTitle 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 |