Note on generalized Archimedes–Borchardt algorithm

Author:

Jarczyk Justyna,Jarczyk WitoldORCID

Abstract

AbstractWe investigate convergence and invariance properties of the generalized Archimedes–Borchardt algorithm. The main tool is reducing the problem to an appropriate Gauss iteration process.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,General Mathematics

Reference25 articles.

1. Borchardt, C.W.: Sur deux algorithmes analogues à celui de la moyenne arithmético-géométrique de deux éléments. In: Memoriam Dominici Chelini, Collect. Math., [etc], L. Cremona. ed. U. Hoepli, Milan, 1881, pp. 206-212

2. reprinted in C.W. Borchardt, Gesammelte Werke, Berlin, pp. 455-462 (1888)

3. Borwein, J.M., Borwein, P.B.: Pi and the AGM. Wiley-Interscience, New York (1998)

4. Bullen, P.S.: Handbook of Means and Their Inequalities. In: Mathematics and Its Applications, vol 560. Kluwer Academic Publishers Group, Dordrecht (2003)

5. Carlson, B.C.: Algorithms involving arithmetic and geometric means. Am. Math. Mon. 78, 496–505 (1971)

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