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)
Journal or Series Name: SIAM journal on scientific computing 
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.
ISSN: 1064-8275
Institute: Mathematik E-10 
Type: (wissenschaftlicher) Artikel
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