Abstract
A multiwavelet basis construction for the interval (0, 1) with the special property that the corresponding wavelet discretization of second order constant coefficient differential operators is sparse, is extended to the realline \(\mathbb{R}\) and the half-space \(\mathbb{R}_{+}\). The advantage of these new bases is their very convenient usage within adaptive wavelet schemes applied to operator problems on unbounded domains as performance of these schemes is increased while their implementation is facilitated. The construction is explained and underlined by selected numerical experiments.
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Acknowledgements
The author is grateful to the DFG Research Training Group 1100 for financial support and would like to thank his PhD advisor Prof. Dr. Karsten Urban.
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Kestler, S. (2013). A Special Multiwavelet Basis for Unbounded Product Domains. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_20
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DOI: https://doi.org/10.1007/978-3-642-33134-3_20
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