Reconstruction of a function from Hermite-Birkhoff data

Birkhoff (or lacunary) interpolation is an extension of polynomial interpolation that appears when observation gives irregular information about some function and its derivatives. A Birkhoff interpolation problem is not always solvable even in the appropriate polynomial or rational space. In this paper we split up the initial problem in subproblems having a unique polynomial solution and use multinode rational basis functions in order to obtain a global interpolant.