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AIMS Mathematics

2025, Volume 10, Issue 2: 3836-3847. doi: 10.3934/math.2025178
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High relative accuracy for a Newton form of bivariate interpolation problems

  • 1.
    Departamento de Matemática Aplicada / IUMA, Universidad de Zaragoza, Spain
  • 2.
    Departamento de Matemática Aplicada / CAPA, Universidad de Zaragoza, Spain
  • Received: 01 January 2025 Revised: 12 February 2025 Accepted: 19 February 2025 Published: 26 February 2025

  • MSC : 15A06, 15A18, 15A23, 65F05, 65G50

  • The problem of bivariate polynomial interpolation using Newton-type bases is examined, leading to the application of a generalized Kronecker matrix product. Algorithms for computing the coefficients of the interpolating polynomial are presented, along with conditions that ensure relative errors of the order of machine precision. A generalization of the classical recursion formula of divided differences in two dimensions is proposed for grids that generalize the standard rectangular layout. Numerical experiments demonstrate the high accuracy achieved by the proposed approach.

    Citation: Yasmina Khiar, Esmeralda Mainar, Eduardo Royo-Amondarain, Beatriz Rubio. High relative accuracy for a Newton form of bivariate interpolation problems[J]. AIMS Mathematics, 2025, 10(2): 3836-3847. doi: 10.3934/math.2025178

    Related Papers:

  • The problem of bivariate polynomial interpolation using Newton-type bases is examined, leading to the application of a generalized Kronecker matrix product. Algorithms for computing the coefficients of the interpolating polynomial are presented, along with conditions that ensure relative errors of the order of machine precision. A generalization of the classical recursion formula of divided differences in two dimensions is proposed for grids that generalize the standard rectangular layout. Numerical experiments demonstrate the high accuracy achieved by the proposed approach.



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