## 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. |

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