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TitleStable monomial basis for multivariate Birkhoff interpolation problems
Author(s) Kai Cui, Landy Rabehasaina
TypeArticle in Journal
AbstractAbstract 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 .
KeywordsBirkhoff interpolation, Stable monomial basis, Empirical points, Admissible perturbation
URL http://www.sciencedirect.com/science/article/pii/S0377042714003914
JournalJournal of Computational and Applied Mathematics
Pages162 - 170
Translation No
Refereed No