Dieter Schott

Projection kernels of linear operators and convergence considerations

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 68, 13 - 43 (2013)

MSC: 47H04   Set-valued operators [See also 28B20, 54C60, 58C06]
  47H09   Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
  65JXX   Numerical analysis in abstract spaces

Abstract:   In the study of iterative methods used to solve linear operator equations sequences of linear iteration operators $(T_k)$ occur which have a nontrivial projection kernel, that is a linear projector $P \neq O$ satisfying $P = T_k P = P T_k$ for all natural $k$. The convergence proof for $(T_k)$ or some related operator sequences is simplified if such $P$ is known. It is investigated when projection kernels exist and how they can be determined. Besides, special types of projection kernels are considered.

Keywords:   Linear operators, FejÚr monotone operators, nonexpansive operators, projectors, orthoprojectors, relaxation of orthoprojectors
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