Qian, Jiang; Wang, Renhong; Zhu, Chungang; Wang, Fan On spline quasi-interpolation in cubic spline space \(S^{1,2}_3(\Delta^{(2)}_{mn})\). (Chinese. English summary) Zbl 1488.65025 Sci. Sin., Math. 44, No. 7, 769-778 (2014). Summary: In this paper, by means of the basis composed of two sets of splines with distinct local supports, cubic spline quasi-interpolating operators are investigated on nonuniform type-2 triangulation. These variation diminishing operators based on five mesh points or the center of the support of each spline \(B^1_{ij}\) and five mesh points of the support of each spline \(B^2_{ij}\) can preserve good approximation, and even reproduce any polynomial of nearly best degrees. Moreover, the spline series can approximate a real sufficiently smooth function uniformly based on the modulus of continuity. And then the convergence results are worked out. Cited in 2 Documents MSC: 65D07 Numerical computation using splines 65D05 Numerical interpolation 41A15 Spline approximation Keywords:bivariate splines; conformality of smoothing cofactor method; nonuniform type-2 triangulation; quasi-interpolation; modulus of continuity PDFBibTeX XMLCite \textit{J. Qian} et al., Sci. Sin., Math. 44, No. 7, 769--778 (2014; Zbl 1488.65025) Full Text: DOI