Abstract
In this paper, a kind of univariate multiquadric quasi-interpolants with the derivatives of approximated function is proposed by combining a univariate multiquadric quasi-interpolant with Lidstone interpolation polynomials proposed in Lidstone (Proc Edinb Math Soc 2:16–19, 1929), Costabile and Dell’ Accio (App Numer Math 52:339–361, 2005) and Catinas (J Appl Funct Anal 4:425–439, 2006). For practical purposes, another kind of approximation operators without any derivative of the approximated function is given using divided differences to approximate the derivatives. Some error bounds and the convergence rates of new operators are derived, which demonstrates that our operators could provide the desired precision by choosing a suitable shape-preserving parameter c and a non-negative integer n. Finally, we make extensive comparison with the other existing methods and give some numerical examples. Moreover, the associated algorithm is easily implemented.
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Acknowledgements
The authors are grateful to the referees for their suggestions. The work was supported by National Natural Science Foundation of China (Grant nos. 61872162 and 11701209), the Open Project of Key Laboratory of Symbolic Computing and Knowledge Engineering of Ministry of Education(Jilin University) (Grant no. 93K172019K13), and the School Level Projection of Jilin University of Finance and Economics (Grant no. 2018B13).
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Communicated by Antonio José Silva Neto.
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Wu, R., Li, H. & Wu, T. Univariate Lidstone-type multiquadric quasi-interpolants. Comp. Appl. Math. 39, 141 (2020). https://doi.org/10.1007/s40314-020-01159-x
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DOI: https://doi.org/10.1007/s40314-020-01159-x