Sparse radial basis function approximation with spatially variable shape parameters.

•A greedy algorithm is proposed for function approximation using a parametrized dictionary of radial basis functions.•Significant reductions in the memory requirement and training cost are achieved using an incremental QR factorization scheme.•The proposed algorithm provides exceptional modeling flexibility via the use of spatially variable shape parameters.•All the model parameters are estimated efficiently in a single run without using expensive cross-validation procedures.