Geodesic
The generalizations of Newton's interpolation formula due to Mühlbach and Andoyer
Electronic transactions on numerical analysis, Tome 2 (1994), pp. 130-137
Newton's formula for constructing the interpolation polynomial is well-known. It makes use of divided differences. It was generalized around 1971-1973 by M$\ddot $uhlbach for interpolation by a linear family of functions forming a complete Chebyshev system. This generalization rests on a generalization of divided differences due to Popoviciu. In this paper, it is shown that M$\ddot $uhlbach's formula is related to the work of Andoyer which goes back to the beginning of the century.
Classification : 65D05, 41A05
Keywords: interpolation, divided differences, biorthogonality 
@article{ETNA_1994__2__a5,
     author = {Brezinski,  C.},
     title = {The generalizations of {Newton's} interpolation formula due to {M\"uhlbach} and {Andoyer}},
     journal = {Electronic transactions on numerical analysis},
     pages = {130--137},
     year = {1994},
     volume = {2},
     zbl = {0852.65006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1994__2__a5/}
}
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Brezinski,  C. The generalizations of Newton's interpolation formula due to Mühlbach and Andoyer. Electronic transactions on numerical analysis, Tome 2 (1994), pp. 130-137. http://geodesic.mathdoc.fr/item/ETNA_1994__2__a5/