Publisher DOI: | 10.1137/18M119063X | Title: | Iterative solution of saddle-point systems from radial basis function (RBF) interpolation | Language: | English | Authors: | Le Borne, Sabine ![]() Wende, Michael |
Keywords: | Hierarchical matrices;Preconditioning;Radial basis function;Saddle-point systems;Scattered data interpolation | Issue Date: | 2019 | Source: | SIAM Journal on Scientific Computing 3 (41): A1706-A1732 (2019) | Abstract (english): | Scattered data interpolation using conditionally positive definite radial basis functions typically leads to large, dense, and indefinite systems of saddle-point type. Due to ill-conditioning, the iterative solution of these systems requires an effective preconditioner. Using the technique of H -matrices, we propose, analyze, and compare two preconditioning approaches: transformation of the indefinite into a positive definite system using either Lagrangian augmentation or the nullspace method combined with subsequent H -Cholesky preconditioning. Numerical tests support the theoretical condition number estimates and illustrate the performance of the proposed preconditioners which are suitable for problems with up to N ≈ 40000 centers in two or three spatial dimensions. |
URI: | http://hdl.handle.net/11420/3379 | ISSN: | 1064-8275 | Institute: | Mathematik E-10 | Document Type: | Article | Journal: | SIAM journal on scientific computing |
Appears in Collections: | Publications without fulltext |
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