Abstract
We consider the interpolation problem for a class of radial basis functions (RBFs) that includes the classical polyharmonic splines (PHS). We show that the inverse of the system matrix for this interpolation problem can be approximated at an exponential rate in the block rank in the \(\mathcal {H}\)-matrix format, if the block structure of the \(\mathcal {H}\)-matrix arises from a standard clustering algorithm.
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Open access funding provided by TU Wien (TUW). NA was funded by the Austrian Science Fund (FWF) Project P 28367 and JMM was supported by the Austrian Science Fund (FWF) by the special research program Taming complexity in PDE systems (Grant SFB F65).
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Communicated by: Tobin Driscoll
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Angleitner, N., Faustmann, M. & Melenk, J.M. \(\mathcal {H}\)-inverses for RBF interpolation. Adv Comput Math 49, 85 (2023). https://doi.org/10.1007/s10444-023-10069-5
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DOI: https://doi.org/10.1007/s10444-023-10069-5