The authors propose preconditioning strategies which diminished number of flops and storage requirements in large radial basis function interpolation problems. The strategy is based on a change of basis to a basis of approximate cardinal functions. The GMRES iterative method for non-symmetric systems is used. Richly illustrated numerical examples are discussed. Possible applications in image wrapping, medical imaging, topography, bathymetry, hydrology, aeromagnetic survey, geophysics and geology, are mentioned.