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On spline quasi-interpolation in cubic spline space \(S^{1,2}_3(\Delta^{(2)}_{mn})\). (Chinese. English summary) Zbl 1488.65025

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.

MSC:

65D07 Numerical computation using splines
65D05 Numerical interpolation
41A15 Spline approximation
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