Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces

In this paper we analyze a greedy procedure to approximate linear functional defined in reproducing kernel Hilbert space by nodal values. This computes quadrature rule which can be applied general functionals. For large class of functionals, that includes integration functionals and other interesting cases, but does not include differentiation, prove convergence results for the approximation means quasi-uniform points generalize various ways several known results. A perturbation analysis weights node computation is also discussed. Beyond theoretical investigations, demonstrate numerically our algorithm effective treating densities, it even very competitive when compared existing methods Uncertainty Quantification.