Using piecewise linear interpolations in spherical harmonic analysis

In this paper an alternative approach to spherical harmonic analysis is investigated which uses piecewise linear interpolations (PLIs) to replace conventional block mean values (BMVs). Detailed formulations for using PLIs in spherical harmonic analysis are systematically developed. Research shows that BMVs give rise to larger errors than PLIs. Error estimations for the two approaches are given, convincingly showing that PLIs yield much better results than BMVs. Many numerical examples are illustrated and numerically show that PLIs are more reliable and applicable than BMVs.