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AIMS Mathematics

2023, Volume 8, Issue 9: 20914-20932. doi: 10.3934/math.20231065
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Research article

Bivariate multiquadric quasi-interpolation operators of Lidstone type

  • 1.
    School of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China
  • 2.
    GongQing Institute Of Science And Technology, Jiujiang 332020, China
  • Received: 13 May 2023 Revised: 14 June 2023 Accepted: 18 June 2023 Published: 30 June 2023

  • MSC : 41A05, 65D05, 65D15

  • In this paper, a kind of bivariate multiquadric quasi-interpolant with the derivatives of a approximated function is studied by combining the known multiquadric quasi-interpolant with the generalized Taylor polynomials that act as the bivariate Lidstone interpolation polynomials. For practical purposes, a kind of improved approximation operator without any derivative of the approximated function is given by using bivariate divided differences to approximate the derivatives. It has the property of high-degree polynomial reproducing. In addition, the improved bivariate quasi-interpolation operators only demand information of the location points rather than the derivatives of the function approximated. Some error bounds in terms of the modulus of continuity of high order and Peano representations for the error are given. Several numerical comparisons with other existing methods are carried out to verify a higher degree of accuracy based on the obtained scheme. Furthermore, the advantage of our method is that the algorithm is very simple and easy to implement.

    Citation: Ruifeng Wu. Bivariate multiquadric quasi-interpolation operators of Lidstone type[J]. AIMS Mathematics, 2023, 8(9): 20914-20932. doi: 10.3934/math.20231065

    Related Papers:

  • In this paper, a kind of bivariate multiquadric quasi-interpolant with the derivatives of a approximated function is studied by combining the known multiquadric quasi-interpolant with the generalized Taylor polynomials that act as the bivariate Lidstone interpolation polynomials. For practical purposes, a kind of improved approximation operator without any derivative of the approximated function is given by using bivariate divided differences to approximate the derivatives. It has the property of high-degree polynomial reproducing. In addition, the improved bivariate quasi-interpolation operators only demand information of the location points rather than the derivatives of the function approximated. Some error bounds in terms of the modulus of continuity of high order and Peano representations for the error are given. Several numerical comparisons with other existing methods are carried out to verify a higher degree of accuracy based on the obtained scheme. Furthermore, the advantage of our method is that the algorithm is very simple and easy to implement.


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