An optimal adaptive wavelet method without coarsening of the iterands |
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| Authors: | Tsogtgerel Gantumur Helmut Harbrecht Rob Stevenson |
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| Institution: | Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands ; Institute of Computer Science and Applied Mathematics, Christian--Albrechts--University of Kiel, Olshausenstr. 40, 24098 Kiel, Germany ; Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands |
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| 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. |
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| Keywords: | Adaptive methods operator equations wavelets optimal computational complexity best $N$-term approximation |
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