Iterative sparse interpolation in reproducing kernel Hilbert spaces

The problem of interpolating data in reproducing kernel Hilbert spaces is well known to be ill-conditioned. In the presence of noise, regularisation can be applied to find a good solution. In the noise-free case, regularisation has the effect of over-smoothing the function and few data points are interpolated. In this paper an alternative framework, based on sparsity, is proposed for interpolation of noise-free data. Iterative construction of a sparse sequence of interpolants is shown to be well defined and produces good results.