RMVPIA: a new algorithm for computing the Lagrange multivariate polynomial interpolation (Q780413)

The multivariate polynomial interpolation problem has been extensively studied over the past 40 years, both in Lagrange version and using Newton's interpolation formula. In this paper the authors focus on the particular case where the interpolation nodes are located in a mesh or grid. To do this, they develop an algorithm called RMVPIA and verify that as in the bivariated case, deleting a node on one of the grid axes preserves the previous calculations used in the interpolation process. Using a general recurrence interpolation formula and its applications (a generalizad Sylvester's identity) to multivariate interpolation gives them the ability to use new arrays that simplify the interpolation process. The development of this work allows one, in a simple way, to generalize the results obtained to multivariate polynomial interpolation with vector values. Other types of multivariate interpolation may be solved with this algorithm by varying the configuration of the interpolation nodes.