Birkhoff interpolation

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.

References

* G. Lorentz, K. Zeller, Birkhoff Interpolation, "SIAM Journal on Numerical Analysis," volume 8, issue 1, March 1971.