A shape-preserving quasi-interpolation operator satisfying quadratic polynomial reproduction property to scattered data |
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Authors: | Renzhong Feng Feng Li |
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Institution: | Department of Mathematics, Beijing University of Aeronutics and Astronautics, Beijing 100083, PR China; Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, PR China |
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Abstract: | In this paper, we construct a univariate quasi-interpolation operator to non-uniformly distributed data by cubic multiquadric functions. This operator is practical, as it does not require derivatives of the being approximated function at endpoints. Furthermore, it possesses univariate quadratic polynomial reproduction property, strict convexity-preserving and shape-preserving of order 3 properties, and a higher convergence rate. Finally, some numerical experiments are shown to compare the approximation capacity of our quasi-interpolation operator with that of Wu and Schaback’s quasi-interpolation scheme. |
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Keywords: | 41A05 41A25 |
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