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Construction of real-time spline quasi-interpolation schemes. (English) Zbl 0692.41014

Summary: Spline quasi-interpolants of the form \(Q(f,x)=\sum_{i}f(t_ i)M'_ i(x)\) are constructed, where \(M'_ i(x)\) are locally supported spline functions with arbitrary knot sequences nodes which may be different from the nodes. Our results show that they approximate sufficiently smooth functions with the optimal order of accuracy. It is important to point out that the structure of these spline quasi-interpolants have computational advantages and provide a useful and efficient tool in realtime applications.

MSC:

41A15 Spline approximation