Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings III: Frames

Details Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings III: Frames Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings III: Frames

2006-11-19

arxiv.org/abs/math/0611569v2

Mathematics

Numerical Analysis

J. Complexity, to appear. Final version, minor mistakes corrected

Scientific paper

We study the optimal approximation of the solution of an operator equation by certain n-term approximations with respect to specific classes of frames. We study worst case errors and the optimal order of convergence and define suitable nonlinear frame widths. The main advantage of frames compared to Riesz basis, which were studied in our earlier papers, is the fact that we can now handle arbitrary bounded Lipschitz domains--also for the upper bounds. Key words: elliptic operator equation, worst case error, frames, nonlinear approximation, best n-term approximation, manifold width, Besov spaces on Lipschitz domains

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