An optimal adaptive wavelet method without coarsening of the iterands

Abstract

In this paper, an adaptive wavelet method for solving linear operator equations is constructed that is a modification of the method from [Math. Comp, 70 (2001), pp. 27-75] by Cohen, Dahmen and DeVore, in the sense that there is no recurrent coarsening of the iterands. Despite this, it will be shown that the method has optimal computational complexity. Numerical results for a simple model problem indicate that the new method is more efficient than an existing alternative adaptive wavelet method.