Discretizing spherical integrals and its applications
Efficient discretization of spherical integrals is required in many numerical methods associated with solving differential and integral equations on spherical domains. In this paper, we discuss a discretization method that works particularly well with convolutions of spherical integrals. We utilize this method to construct spherical basis function networks, which are subsequently employed to approximate the solutions of a variety of differential and integral equations on spherical domains. We show that, to a large extend, the approximation errors depend only on the smoothness of the spherical basis function. We also derive error estimates of the pertinent approximation schemes. As an application, we discuss a Galerkin type solutions for spherical Fredholm integral equations of the first kind, and obtain rates of convergence of the spherical basis function networks to the solutions of these equations.
Approximation, Fredholm integral equation, Sphere, Spherical basis function, Spherical convolution
Lin, Shaobo, Xingping Sun, and Zongben Xu. "Discretizing spherical integrals and its applications." In Conference Publications, vol. 2013, no. special, p. 499. American Institute of Mathematical Sciences, 2013.
Discrete and Continuous Dynamical Systems - Series S