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

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. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper proposes a generalized regularized least-squares radial basis approximation for noisy data, which is applied to the numerical solution of stochastic elliptic PDEs. Numerical observations suggest that the method is more stable than typical kernel-based methods.