Regularized Least Squares Approximations on the Sphere Using Spherical Designs
Regularized Least Squares Approximations on the Sphere Using Spherical Designs
We consider polynomial approximation on the unit sphere $\mathbb{S}^2=\{(x,y,z)\in \mathbb{R}^3:x^2+y^2+z^2=1\}$ by a class of regularized discrete least squares methods with novel choices for the regularization operator and the point sets of the discretization. We allow different kinds of rotationally invariant regularization operators, including the zero operator (in which case the …