15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Sektion 7 - Funktionalanalysis, Harmonische Analysis
Donnerstag, 20. September 2001, 16.30, Hörsaal 28


Parallel methods for finding common fixed points of projections and paracontractions

Gilbert Crombez, Ghent University


The method of Pierra [2] in the theory of projections onto convex sets to view parallel iterations as sequential ones in a suitable product space, leads to extensions in at least two different directions: (i) the flexibility of the method may be used to construct an algorithm in which the monotoneous behaviour of the converging sequence is interrupted at different steps in the iteration, but that nevertheless may lead to fast convergence; (ii) the underlying ideas of the method may be used to construct parallel algorithms for operators that are more general than projections, such as paracontractions [1]. In our talk we comment on these extensions.

[1] L. Elsner, I. Koltracht and M. Neumann, ``Convergence of sequential and asynchronous nonlinear paracontractions'', Numer. Math. 62 (1992), 305-319.
[2] G. Pierra, ``Decomposition through formalization in a product space'', Math. Programming 28 (1984), 96-115.

E-Mail: Gilbert.Crombez@rug.ac.be

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