Preprint Article Version 1 NOT YET PEER-REVIEWED

Quasi-Interpolation Operators for Bivariate Quintic Spline Spaces and Their Applications

Version 1 : Received: 12 January 2017 / Approved: 12 January 2017 / Online: 12 January 2017 (10:04:06 CET)

A peer-reviewed article of this Preprint also exists.

Yu, R.; Zhu, C.; Hou, X.; Yin, L. Quasi-Interpolation Operators for Bivariate Quintic Spline Spaces and Their Applications. Math. Comput. Appl. 2017, 22, 10. Yu, R.; Zhu, C.; Hou, X.; Yin, L. Quasi-Interpolation Operators for Bivariate Quintic Spline Spaces and Their Applications. Math. Comput. Appl. 2017, 22, 10.

Journal reference: Math. Comput. Appl. 2017, 22, 10
DOI: 10.3390/mca22010010

Abstract

Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces S53 (∆mn(2)). Moreover, the properties of the proposed quasi-interpolation operators are studied, as well as its applications for solving two-dimensional Burgers’ equation and image reconstruction. Some numerical examples show that these methods, which are easy to implement, provide accurate results.

Subject Areas

bivariate spline space; quasi-interpolation operator; type-2 triangulation 3; burgers’ equations; image reconstruction

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