Local multilevel scattered data interpolation

Radial basis functions play an increasingly prominent role in modern approximation. They are widely used in scattered data fitting, numerical solution of partial differential equations, machine learning and others. Although radial basis functions have excellent approximation properties, they often produce highly ill-conditioned discrete algebraic system and lead to a high computational cost. The paper introduces local multilevel scattered data interpolation method, which employ nested scattered data sets and scaled compactly supported radial basis functions with varying support radii. We will provide convergence theory for Sobolev target functions. And several numerical experiments will be provided to conform the efficiency of new method.