A Novel Recursive Modification Framework for Enhancing Polynomial Reproduction Property of Interpolation Basis Functions

Abstract

In this work, we construct a novel recursive modification framework for enhancing the polynomial reproduction property of interpolation basis functions. A general scheme for constructing local approximation and interpolation basis functions without solving a linear system of equations is also developed. Some illustrative examples are given to show the effectiveness and practicability of the new proposed schemes for modifying interpolation basis functions.