Optimal adaptive computations in the Jaffard algebra and localized frames

摘要: We study the numerical solution of infinite matrix equations Au=f for a A in Jaffard algebra. These matrices appear naturally via frame discretizations many applications such as Gabor analysis, sampling theory, and quasi-diagonalization pseudo-differential operators weighted Sjostrand class. The proposed algorithm has two main features: firstly, it converges to with quasi-optimal order complexity respect classes localized vectors; secondly, addition @?^2-convergence, automatically some stronger norms @?^p-spaces. As an application we approximate canonical dual show that this approximation is again frame, even atomic decomposition class associated Banach spaces. tools are taken from adaptive algorithms, theory frames, special algebra properties