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A New Approach to General Interpolation Formulae for Bivariate Interpolation

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  • Le Zou
  • Shuo Tang

Abstract

General interpolation formulae for bivariate interpolation are established by introducing multiple parameters, which are extensions and improvements of those studied by Tan and Fang. The general interpolation formulae include general interpolation formulae of symmetric branched continued fraction, general interpolation formulae of univariate and bivariate interpolation, univariate block based blending rational interpolation, bivariate block based blending rational interpolation and their dual schemes, and some interpolation form studied by many scholars in recent years. We discuss the interpolation theorem, algorithms, dual interpolation, and special cases and give many kinds of interpolation scheme. Numerical examples are given to show the effectiveness of the method.

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  • Le Zou & Shuo Tang, 2014. "A New Approach to General Interpolation Formulae for Bivariate Interpolation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, June.
    • Handle: RePEc:hin:jnlaaa:421635
    DOI: 10.1155/2014/421635
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    Cited by:

    1. Le Zou & Liangtu Song & Xiaofeng Wang & Yanping Chen & Chen Zhang & Chao Tang, 2020. "Bivariate Thiele-Like Rational Interpolation Continued Fractions with Parameters Based on Virtual Points," Mathematics, MDPI, vol. 8(1), pages 1-21, January.

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