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arXiv · 1901.00654

A Multigrid Preconditioner for Tensor Product Spline Smoothing

Martin Siebenborn·Julian Wagner
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Abstract

Uni- and bivariate data smoothing with spline functions is a well established method in nonparametric regression analysis. The extension to multivariate data is straightforward, but suffers from exponentially increasing memory and computational complexity. Therefore, we consider a matrix-free implementation of a geometric multigrid preconditioned conjugate gradient method for the regularized least squares problem resulting from tensor product B-spline smoothing with multivariate and scattered data. The algorithm requires a moderate amount of memory and is therefore applicable also for high-dimensional data. Moreover, for arbitrary but fixed dimension, we achieve grid independent convergence which is fundamental to achieve algorithmic scalability.

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Martin Siebenborn, Julian Wagner. 2019-01-03. A Multigrid Preconditioner for Tensor Product Spline Smoothing. https://doi.org/10.1007/s00180-021-01104-4

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