Discrete Least Squares Hybrid Approximation with Regularization on the Two-Sphere

Abstract

In this paper we consider the discrete constrained least squares problem coming from numerical approximation by hybrid scheme on the sphere, which applies both radial basis functions and spherical polynomials. We propose a novel $l_2-l_1$ regularized least square model for this problem and show that it is a generalized model of the classical "saddle point" model. We apply the alternating direction algorithm to solve the $l_2-l_1$ model and propose a convenient stopping criterion for the algorithm. Numerical results show that our model is more efficient and accurate than other models.