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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An optimal adaptive wavelet method without coarsening of the iterands


Authors: Tsogtgerel Gantumur, Helmut Harbrecht and Rob Stevenson
Journal: Math. Comp. 76 (2007), 615-629
MSC (2000): Primary 41A25, 41A46, 65F10, 65T60
Published electronically: November 27, 2006
MathSciNet review: 2291830
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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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Additional Information

Tsogtgerel Gantumur
Affiliation: Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands
Email: gantumur@math.uu.nl

Helmut Harbrecht
Affiliation: Institute of Computer Science and Applied Mathematics, Christian–Albrechts–Uni- versity of Kiel, Olshausenstr. 40, 24098 Kiel, Germany
Email: hh@numerik.uni-kiel.de

Rob Stevenson
Affiliation: Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands
Email: stevenson@math.uu.nl

DOI: http://dx.doi.org/10.1090/S0025-5718-06-01917-X
PII: S 0025-5718(06)01917-X
Keywords: Adaptive methods, operator equations, wavelets, optimal computational complexity, best $N$-term approximation
Received by editor(s): March 22, 2005
Received by editor(s) in revised form: January 25, 2006
Published electronically: November 27, 2006
Additional Notes: This work was supported by the Netherlands Organization for Scientific Research and by the EC-IHP project “Breaking Complexity”
Article copyright: © Copyright 2006 American Mathematical Society