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

In this paper, we modify the classical cubic B-spline quasi-interpolant Q(3) by utilizing multi-node higher-order expansions and the P-t-exact A-discretization approach. The proposed quartic spline quasi-interpolant Q(3)(1) 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.

Automated summary

In this paper, we propose a modification to the classical cubic B-spline quasi-interpolant Q(3) by using multi-node higher-order expansions and the P-t-exact A-discretization approach. The proposed quartic spline quasi-interpolant Q(3)(1) achieves higher accuracy with relatively small computational complexity, without requiring any additional information of the target function. We also develop high accuracy quadrature formulas and differentiation matrices using the proposed quasi-interpolant, providing explicit coefficient error estimates. Numerical experiments demonstrate the effectiveness of the proposed quasi-interpolants.