2024/08/27 by Zhengjie Sun, Sun, Zhengjie, Wenwu Gao +3 · 1 citation
Engineering · Physics and Astronomy · #41A25 #41A55 #43A90 #65D12 #65D32 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2408.14803
openalex publication_date 2024/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose and study a new quasi-interpolation method on spheres featuring the following two-phase construction and analysis. In Phase I, we analyze and characterize a large family of zonal kernels (e.g., the spherical version of Poisson kernel, Gaussian, compactly-supported radial kernels), so that the underlying spherical convolution operators (upon the introduction of a scaling parameter) attains a high-order of approximation to target functions. In Phase II, we discretize the spherical integrals utilizing quadrature rules of optimal order to produce the final quasi-interpolants. Numerical experiments demonstrate that the new quasi-interpolation algorithm is robust and amenable to integrated as well as distributed ways of implementation. Moreover, the underlying error-analysis shows that by fine-tuning the scaling parameter in the radial kernels employed, the resulting quasi-interpolants achieve a well-balanced trade-off between approximation and sampling errors.