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Iterative solution of saddle-point systems from radial basis function (RBF) interpolation
Publikationstyp
Journal Article
Date Issued
2019
Sprache
English
Author(s)
Institut
TORE-URI
Volume
41
Issue
3
Start Page
A1706
End Page
A1732
Citation
SIAM Journal on Scientific Computing 3 (41): A1706-A1732 (2019)
Publisher DOI
Scopus ID
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.
Subjects
Hierarchical matrices
Preconditioning
Radial basis function
Saddle-point systems
Scattered data interpolation