Generalized regularized least-squares approximation of noisy data with application to stochastic PDEs

Abstract

The regularized least-squares radial basis approximation is a kernel-based method to approximate a set of scattered data by a least-squares fit based on an optimization procedure that balances a tradeoff between smoothness of approximation and closeness to the data via a smoothing parameter. This paper suggests the generalized regularized least-squares radial basis approximation for noisy data and its application to the numerical solution of stochastic elliptic PDEs. Numerical observations show that the proposed method is more stable than the typical kernel-based method.