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arXiv · 2503.04914

Efficiently parallelizable kernel-based multi-scale algorithm

Federico Lot·Christian Rieger
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Abstract

The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventional kernel-based interpolation techniques. The multi-scale method is based of an hierarchy of point clouds and compactly supported radial basis functions, typically Wendland functions. There is a rich body of literature concerning the analysis of this method including error estimates. This article addresses the efficient parallelizable implementation of those methods. To this end, we present and analyse a monolithic approach to compute the kernel-based multi-scale approximation.

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Federico Lot, Christian Rieger. 2025-03-06. Efficiently parallelizable kernel-based multi-scale algorithm. https://arxiv.org/abs/2503.04914

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