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On the approximation power of bivariate quadratic \(C^1\) splines. (English) Zbl 0980.41009
Authors’ abstract: In this paper we investigate the approximation power of local bivariate quadratic \(C^1\) quasi-interpolating \((q-1)\) spline operators with a four-directional mesh. In particular, we show that they can approximate a real function and its partial derivatives up to an optimal order and we derive local and global upper bounds both for the errors and for the spline partial derivatives, in the case the spline is more differentiable than the function. Then such general results are applied to prove new properties of two intersecting \(q - i\) spline operators, proposed and partially studied in C. K. Chui and R. Wang [Sci. Sin. 27, Ser. A 1129-1142 (1984; Zbl 0559.41010)].
Reviewer: E.Deeba (Houston)

MSC:
41A15 Spline approximation
Keywords:
spline
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