High accuracy B-spline quasi-interpolants and applications in numerical analysis

Abstract

In this paper, we modify the classical cubic B-spline quasi-interpolant by utilizing multi-node higher-order expansions and the -exact A-discretization approach. The proposed quartic spline quasi-interpolant possesses higher accuracy with small computational complexity increased, while requires no additional information of the target function. Applying the proposed quasi-interpolant, we develop high accuracy quadrature formulas and the differentiation matrices. All corresponding error estimates with explicit coefficients are provided. Numerical experiments illustrate the effectiveness of the proposed quasi-interpolants.