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Some performances of local bivariate quadratic $$C^1$$ quasi-interpolating splines on nonuniform type-2 triangulations. (English) Zbl 1065.65012
The paper is concerned with spline approximations in two dimensions. Continuously differentiable quadratic B-splines are used as basis functions for an approximation by quasi-interpolation. The triangulations on which the B-splines are based are nonuniform and of type-2. The data points at which the approximated values are evaluated are mesh points in the support or close to the support of the B-splines, and there is a fixed number of them which are used. For this set-up, the approximated values orders are established which are nearly optimal. Also, the convergence is shown both for the approximand and for its partial derivatives. Finally, several numerical examples for the quasi-interpolants are presented.

##### MSC:
 65D07 Numerical computation using splines 41A25 Rate of convergence, degree of approximation 65D10 Numerical smoothing, curve fitting 41A15 Spline approximation 41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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