Trivariate Polynomial Natural Spline for 3D Scattered Data Hermit Interpolation (Communications in Mathematical Research, 2021)
Consider a kind of Hermit interpolation for scattered data of 3D bytrivariate polynomial natural spline, such that the objective energy functional (withnatural boundary conditions) is minimal. By the spline function methods in Hilbertspace and variational theory of splines, the characters of the interpolation solution andhow to construct it are studied. One can easily find that the interpolation solution isa trivariate polynomial natural spline. Its expression is simple and the coefficients canbe decided by a linear system. Some numerical examples are presented to demonstrateour methods.
Keywords: scattered data; Hermit interpolation; natural spline.