Birkhoff interpolation

In mathematics, Birkhoff interpolation is an extension of polynomial interpolation. It refers to the problem of finding a polynomial p of degree d such that certain derivatives have specified values at specified points:

where the data points and the nonnegative integers are given. It differs from Hermite interpolation in that it is possible to specify derivatives of p at some points without specifying the lower derivatives or the polynomial itself. The name refers to George David Birkhoff, who first studied the problem in Birkhoff (1906).