An algorithm for the Hermite-Birkhoff interpolation is presented, which reduces the problem to the Hermite interpolation. The missing values and derivatives are expressed by some of the given values and calculated from a system of linear equations. The system itself and its right-hand sides are computed from a set of Hermite interpolation problems. The needed values and derivatives of the Hermite interpolation polynomial can be computed using the algorithm given in the Appendix.
 J. Fiala: Interpolation with prescribed values of derivatives instead of function values
. Apl. mat. 16 (1971) 421-430. MR 0292261
| Zbl 0224.65002
 I. S. Berezin N. P. Židkov: Methods of Computations I. (Russian). M 1959.