On Polynomial Interpolation in the Points of a Geometric Progression, Stirling, Schellbach, Runge and Romberg.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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It is very well known Newtons interpolation series with divided differences simplifies considerably in the case that we interpolate in the points of an arithmetic progression. It seems much less known that a similar simplification occurs in the case when the points of interpolation form a geometric progression. We describe here the practically forgotten work of Stirling 1730, Schellbach 1864, and Runge 1981, and its connection with the elegant and more recent algorithm of Romberg 1955. Author
- Theoretical Mathematics