|Publisher DOI:||10.1137/18M119063X||Title:||Iterative solution of saddle-point systems from radial basis function (RBF) interpolation||Language:||English||Authors:||Le Borne, Sabine
|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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