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An optimal adaptive wavelet method without coarsening of the iterands. (English) Zbl 1115.41023
In this paper, an adaptive wavelet method for solving linear operator equations is presented that is a modification of the method of A. Cohen, W. Dahmen and R. DeVore [Math. Comput. 70, No. 233, 27–75 (2001; Zbl 0980.65130)], in the sense that there is no recurrent coarsening of the iterands. Despite this, it is shown that this method has optimal computational complexity. Numerical results for a simple boundary value problem indicate that the new method is more efficient than an existing adaptive wavelet method.

MSC:
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65F10 Iterative numerical methods for linear systems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65T60 Numerical methods for wavelets
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