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 3 5 p∆ p2q mn q. 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.
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 3 5 (∆ (2) mn ). 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.
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