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

1
College of Information and Management Science, Henan Agricultural University, Zhengzhou 450000, China
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School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
*
Author to whom correspondence should be addressed.
Academic Editor: Fazal M. Mahomed
Math. Comput. Appl. 2017, 22(1), 10; https://doi.org/10.3390/mca22010010
Received: 10 October 2016 / Revised: 19 December 2016 / Accepted: 27 December 2016 / Published: 19 January 2017
(This article belongs to the Special Issue Information and Computational Science)
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 S 5 3 ( Δ m n ( 2 ) ) . Moreover, the properties of the proposed quasi-interpolation operators are studied, as well as its applications for solving the two-dimensional Burgers’ equation and image reconstruction. Some numerical examples show that these methods, which are easy to implement, provide accurate results. View Full-Text
Keywords: bivariate spline space; quasi-interpolation operator; Type-2 triangulation; Burgers’ equations; image reconstruction bivariate spline space; quasi-interpolation operator; Type-2 triangulation; Burgers’ equations; image reconstruction
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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.

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