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An optimal adaptive wavelet method without coarsening of the iterands
Author(s):
Tsogtgerel
Gantumur;
Helmut
Harbrecht;
Rob
Stevenson.
Journal:
Math. Comp.
76
(2007),
615-629.
MSC (2000):
Primary 41A25, 41A46, 65F10, 65T60
Posted:
November 27, 2006
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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.
References:
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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--University 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:
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
Posted:
November 27, 2006
Additional Notes:
This work was supported by the Netherlands Organization for Scientific Research and by the EC-IHP project ``Breaking Complexity''
Copyright of article:
Copyright
2006,
American Mathematical Society
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