On the Approximation of the Derivatives of Spline Quasi-Interpolation in Cubic Spline Space. Issue 1 (February 2014)

• Record Type: Journal Article
• Authors: Qian, Jiang; Wang, Fan
• Is Part Of: Numerical mathematics. Volume 7:Issue 1(2014)
• Page Start: 1
• Page End: 22
• Publication Date: 2014-02
• Subjects: 65D07, -- 41A25; Bivariate splines, -- conformality of smoothing cofactor method, -- nonuniform type-2 triangulation, -- quasi-interpolation, -- modulus of continuity; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.1017/S100489790000026X
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: In this paper, based on the basis composed of two sets of splines with distinct local supports, cubic spline quasi-interpolating operators are reviewed on nonuniform type-2 triangulation. The variation diminishing operator is defined by discrete linear functionals based on a fixed number of triangular mesh-points, which can reproduce any polynomial of nearly best degrees. And by means of the modulus of continuity, the estimation of the operator approximating a real sufficiently smooth function is reviewed as well. Moreover, the derivatives of the nearly optimal variation diminishing operator can approximate that of the real sufficiently smooth function uniformly over quasi-uniform type-2 triangulation. And then the convergence results are worked out.