Birkhoff interpolation

Summary

Birkhoff interpolation asks for a polynomial whose derivatives of chosen orders take chosen values at chosen nodes. Unlike Hermite interpolation, it does not require that all lower derivatives are also prescribed. It contains polynomial interpolation and Hermite interpolation as special cases. Unlike these, it does not always have a unique solution, even when the number of conditions equals the number of coefficients. The main question of the theory is which patterns of conditions, encoded in an incidence matrix, are poised, that is, solvable uniquely for all data.