Optimal polynomial meshes and Caratheodory-Tchakaloff submeshes on the sphere
arXiv:1612.049525 citationsh-index: 27
Originality Synthesis-oriented
AI Analysis
Provides theoretical foundation and practical submeshes for polynomial approximation on the sphere, relevant to numerical analysis and approximation theory.
The paper proves that good covering point configurations on the 2-sphere are optimal polynomial meshes using Dubiner distance, and extracts Caratheodory-Tchakaloff submeshes for compressed least squares fitting.
Using the notion of Dubiner distance, we give an elementary proof of the fact that good covering point configurations on the 2-sphere are optimal polynomial meshes. From these we extract Caratheodory-Tchakaloff (CATCH) submeshes for compressed Least Squares fitting.