The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 19, Number 2 (1948), 207-219.
Solution of Equations by Interpolation
The present paper deals with the numerical solution of equations by the combined use of Newton's method and inverse interpolation. In Part I the case of one equation in one unknown is discussed. The methods described here were developed by Aitken  and Neville , but do not seem as widely known as they should be, perhaps because the original papers are not readily available. (A short summary of Aitken's work will be found in a recent paper by Womersley .) Mention should also be made of an interesting paper by Spoerl , which treats the same problem from a somewhat different viewpoint. In Part II these methods are extended to sets of simultaneous equations.
Ann. Math. Statist., Volume 19, Number 2 (1948), 207-219.
First available in Project Euclid: 28 April 2007
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Kincaid, W. M. Solution of Equations by Interpolation. Ann. Math. Statist. 19 (1948), no. 2, 207--219. doi:10.1214/aoms/1177730245. https://projecteuclid.org/euclid.aoms/1177730245