Stable monomial basis for multivariate Birkhoff interpolation problems

• Kai Cui ^[1] ; Na Lei ^[1]
  1. [1] Jilin University

     Jilin University

     China

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 277, Nº 1 (15 March 2015), 2015, págs. 162-170
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.09.002
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• Resumen

  • For a given node set Z and the corresponding interpolation conditions, one of the key problems in multivariate Birkhoff interpolation is determining a monomial basis that spans the interpolation space. However, a slight perturbation of the node set will result in a different monomial basis. We propose a more general multivariate Birkhoff interpolation scheme and provide a numerical algorithm that can determine the stable monomial basis to ensure that the interpolation polynomial always exists in the space spanned by the monomial basis for any perturbation of the node set within a given error ε.