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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.
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