Quasi-interpolation in Spline Spaces: Local Stability and Approximation Properties

M. E. Castillo, E. M. Garau


In this work we analyze the approximation error in Sobolev norms for quasi-interpolation operators in spline spaces. We establish in a general way the hypotheses on a quasi-interpolant to achieve the optimal order of approximation. Finally, we propose simple but general constructions of such operators that satisfy the established hypotheses and illustrate their performance through some numerical tests.


spline approximation; quasi-interpolation; stability, B-splines

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DOI: https://doi.org/10.5540/tcam.2022.024.01.00009

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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)


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