A fast algorithm for the multivariate Birkhoff interpolation problem

Authors:
Na Lei;Junjie Chai;Peng Xia;Ying Li
Affiliations:
-;-;-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

Multivariate Birkhoff interpolation is the most complicated polynomial interpolation problem and the theory about it is far from systematic and complete. In this paper we derive an Algorithm B-MB (Birkhoff-Monomial Basis) and prove B-MB giving the minimal interpolation monomial basis w.r.t. the lexicographical order of the multivariate Birkhoff problem. This algorithm is the generalization of Algorithm MB in [L. Cerlinco, M. Mureddu, From algebraic sets to monomial linear bases by means of combinatorial algorithms, Discrete Math. 139 (1995) 73-87] which is a well known fast algorithm used to compute the interpolation monomial basis of the Hermite interpolation problem.