Birkhoff interpolation

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In mathematics, Birkhoff interpolation is an extension of polynomial interpolation. It refers to the problem finding a polynomial p of degree d such that

$p^{(n_i)}(x_i) = y_i \qquad\mbox{for } i=1,\ldots,d,$

where the data points $(x i, y i)$ and the nonnegative integers $n i$ are given. It differs from Hermite interpolation in that it is possible to specify derivatives of p at some points without specifying the lower derivates or the polynomial itself.