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The following interpolation problem is considered: There are given points and at some of them the functional values are prescribed. At the other points only the values of the derivatives are given. Some conditions for existence and uniqueness are formulated and the problem is reduced to the problem of solving a system of linear equations for the unknown function values. An algorithm for finding the matrix and the right hand side of this system is suggested which uses an interpolation method for finding the derivatives of the given interpolation polynomial.
[1] G. N. Lance: Numerical methods for high speed computers. London 1960. MR 0128051
[2] L. Boothroyd: Algorithms 10, 11. The Соmр. J. 9 (1966) 211-212.
[3] J. Fiala: Neville-Aitkenova iterační interpolace. Program a zpráva 7-00-40, VLD, Praha 1964.
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