A Matrix-Free Multigrid Preconditioner for Spline Smoothing
c(
person("Martin", "Siebenborn", role = c("aut", "cre", "cph"),
email = "martin.siebenborn@uni-hamburg.de"),
person("Julian", "Wagner", role = c("aut", "cph"),
email = "juwagn89@gmail.com")
)
Data smoothing with penalized splines is a popular method and is well established for one- or two-dimensional covariates. The extension to multiple covariates is straightforward but suffers from exponentially increasing memory requirements and computational complexity. This toolbox provides a matrix-free implementation of a conjugate gradient (CG) method for the regularized least squares problem resulting from tensor product B-spline smoothing with multivariate and scattered data. It further provides matrix-free preconditioned versions of the CG-algorithm where the user can choose between a simpler diagonal preconditioner and an advanced geometric multigrid preconditioner. The main advantage is that all algorithms are performed matrix-free and therefore require only a small amount of memory. For further detail see Siebenborn & Wagner (2019) <arXiv:1901.00654>.
Martin Siebenborn [aut, cre, cph],
Julian Wagner [aut, cph]

Data smoothing with penalized splines is a popular method and is well established for one- or two-dimensional covariates. The extension to multiple covariates is straightforward but suffers from exponentially increasing memory requirements and computational complexity. This toolbox provides a matrix-free implementation of a conjugate gradient (CG) method for the regularized least squares problem resulting from tensor product B-spline smoothing with multivariate and scattered data. It further provides matrix-free preconditioned versions of the CG-algorithm where the user can choose between a simpler diagonal preconditioner and an advanced geometric multigrid preconditioner. The main advantage is that all algorithms are performed matrix-free and therefore require only a small amount of memory. For further detail see Siebenborn & Wagner (2021).