Le Borne, SabineSabineLe BorneWende, MichaelMichaelWende2019-04-162019-04-162019-02-15Computers and Mathematics with Applications 4 (77): 1178-1196 (2019-02-15)http://hdl.handle.net/11420/2327Scattered data interpolation using conditionally positive definite radial basis functions (RBFs) requires the solution of a symmetric saddle-point system. Based on an approximation of the system matrix as a hierarchical matrix, we solve the system iteratively using the GMRes algorithm and a domain decomposition preconditioner. The novelty of our work lies in the proposed solution of the subdomain problems using the nullspace method with an orthogonal basis represented as a sequence of Householder reflectors. The resulting positive definite subdomain systems are solved either directly or using an inner GMRes iteration with H-Cholesky preconditioning. Numerical tests demonstrate the effectiveness of this solution process for up to N=160000 centers in two and three dimensions.en0898-12212019411781196Journal Article10.1016/j.camwa.2018.10.042Other