This algorithm improves approximation efficiency in scattered data using multiscale methods and point clouds, suggesting promising applications in computational tasks.
The kernel-based multiscale 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 multiscale method is based on a 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 presents a nonsequential formulation of the multiscale algorithm, which is efficient to implement as it is parallelizable and allows a natural compression of the resulting matrices. Moreover, we present the theoretical numerical analysis for our new variant of the multiscale method.
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Lot et al. (2025) studied this question.
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