Le Borne, SabineSabineLe BorneWende, MichaelMichaelWende2019-09-182019-09-182019SIAM Journal on Scientific Computing 3 (41): A1706-A1732 (2019)http://hdl.handle.net/11420/3379Scattered 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.en1064-827520193A1706A1732Hierarchical matricesPreconditioningRadial basis functionSaddle-point systemsScattered data interpolationJournal Article10.1137/18M119063XOther