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On the construction of sparse tensor product spaces

Authors: Michael Griebel and Helmut Harbrecht
Journal: Math. Comp. 82 (2013), 975-994
MSC (2010): Primary 41A17, 41A25, 41A30, 41A65
Published electronically: August 9, 2012
MathSciNet review: 3008845
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Abstract: Let $ \Omega _1\subset \mathbb{R}^{n_1}$ and $ \Omega _2\subset \mathbb{R}^{n_2}$ be two given domains and consider on each domain a multiscale sequence of ansatz spaces of polynomial exactness $ r_1$ and $ r_2$, respectively. In this paper, we study the optimal construction of sparse tensor products made from these spaces. In particular, we derive the resulting cost complexities to approximate functions with anisotropic and isotropic smoothness on the tensor product domain $ \Omega _1\times \Omega _2$. Numerical results validate our theoretical findings.

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Additional Information

Michael Griebel
Affiliation: Institut für Numerische Simulation, Universität Bonn, Wegelerstr. 6, 53115 Bonn, Germany

Helmut Harbrecht
Affiliation: Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland

Received by editor(s): May 27, 2011
Received by editor(s) in revised form: September 26, 2011, and October 15, 2011
Published electronically: August 9, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.