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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
:$p^\{(n\_i)\}(x\_i)\; =\; y\_i\; qquadmbox\{for\; \}\; i=1,ldots,d,$
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.

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References

★ G. Lorentz, K. Zeller, Birkhoff Interpolation, ''SIAM Journal on Numerical Analysis,'' volume 8, issue 1.