A Multigrid Preconditioner for Tensor Product Spline Smoothing
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866929640739700736 |
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| author | Siebenborn, Martin Wagner, Julian |
| author_facet | Siebenborn, Martin Wagner, Julian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1901_00654 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Multigrid Preconditioner for Tensor Product Spline Smoothing Siebenborn, Martin Wagner, Julian Numerical Analysis Optimization and Control 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. |
| title | A Multigrid Preconditioner for Tensor Product Spline Smoothing |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/1901.00654 |