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

Abstract

In this paper, we modify the classical cubic B-spline quasi-interpolant $Q_3$ by utilizing multi-node higher-order expansions and the ${\mathbb{P}}_t$-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.

Keywords:

• B-spline
• quasi-interpolation
• polynomial reproduction
• numerical differentiation
• numerical integration

2020 Mathematics Subject Classifications:

• 65D07
• 41A25

Acknowledgements

The authors appreciate the anonymous reviewers for the valuable comments that helped to improve the clarity of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China (Grant Numbers 12071057, 11671068, 12001487) and the Characteristic & Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University- Statistics).