Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773775 | Journal of Approximation Theory | 2017 | 31 Pages |
Abstract
In this paper we establish a multiscale approximation for random fields on the sphere using spherical needlets-a class of spherical wavelets. We prove that the semidiscrete needlet decomposition converges in mean and pointwise senses for weakly isotropic random fields on Sd, dâ¥2. For numerical implementation, we construct a fully discrete needlet approximation of a smooth 2-weakly isotropic random field on Sd and prove that the approximation error for fully discrete needlets has the same convergence order as that for semidiscrete needlets. Numerical examples are carried out for fully discrete needlet approximations of Gaussian random fields and compared to a discrete version of the truncated Fourier expansion.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Quoc T. Le Gia, Ian H. Sloan, Yu Guang Wang, Robert S. Womersley,