Le Borne, SabineSabineLe Borne2019-09-032019-09-032019SIAM Journal on Matrix Analysis and Applications 2 (40): 517-541 (2019)http://hdl.handle.net/11420/3272Radial basis function (RBF) interpolation is a powerful, meshfree tool for function approximation but its direct implementation might suffer from severe ill-conditioning as the shape parameter decreases. We build upon RBF-GA, a stable approach for Gaussian RBFs, and derive its representation in terms of a matrix factorization which can then be generalized to a symmetrized version. This symmetrized version requires fewer function evaluations, yields new insight into the flat limit case, and, combined with diagonal scaling, allows a further reduction of the condition number. We also propose a truncated version of the basis transformation. We conclude with numerical tests to illustrate the performance of all introduced interpolation methods.en0895-479820192517541FactorizationIll-conditioningKernel-based interpolationRadial basis functionStableSymmetrizationTruncationJournal Article10.1137/18M119207XOther