Abstract
Greedy kernel approximation algorithms are successful techniques for sparse and accurate data-based modelling and function approximation. Based on a recent idea of stabilization (Wenzel et al., A novel class of stabilized greedy kernel approximation algorithms: convergence, stability & uniform point distribution. e-prints. arXiv:1911.04352, 2019) of such algorithms in the scalar output case, we here consider the vectorial extension built on VKOGA (Wirtz and Haasdonk, Dolomites Res Notes Approx 6:83–100, 2013. We introduce the so called γ-restricted VKOGA, comment on analytical properties and present numerical evaluation on data from a clinically relevant application, the modelling of the human spine. The experiments show that the new stabilized algorithms result in improved accuracy and stability over the non-stabilized algorithms.
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Notes
- 1.
This corresponds to the case of using separable matrix-valued kernels, i.e. K(x, y) := k(x, y) ⋅ I where I is the d × d identity matrix [14].
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The authors acknowledge the funding of the project by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2075 - 390740016.
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Haasdonk, B., Wenzel, T., Santin, G., Schmitt, S. (2021). Biomechanical Surrogate Modelling Using Stabilized Vectorial Greedy Kernel Methods. 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_49
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