Abstract
When using kernel interpolation techniques for constructing a surrogate model from given data, the choice of interpolation points is crucial for the quality of the surrogate. When dealing with vector-valued target functions which are approximated by matrix-valued kernel models, the selection problem is further complicated as not only the choice of points but also the directions in which the data is projected must be determined.
We thus propose variants of Matrix P-greedy algorithms that enable us to iteratively select suitable sets of point-direction pairs with which the approximation space is enriched. We show that the selected pairs result in quasi-optimal convergence rates. Experimentally, we investigate the approximation quality of the different variants.
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Acknowledgements
The authors acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC 2075—390740016.
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Wittwar, D., Haasdonk, B. (2021). Convergence Rates for Matrix P-Greedy Variants. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_119
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DOI: https://doi.org/10.1007/978-3-030-55874-1_119
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