Arithmetic-geometric mean algorithm
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Abstract
The arithmetic-geometric mean algorithm introduced by Gauss is a remarkable example of approximation of a multivalued transcendental function by means of an algebraic function. In Gauss's works published during his lifetime and in the remaining posthumous materials, almost no attention is paid to the convergence of the algorithm and the branching of its terms is not considered at all.
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(Archived) Articles
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References
- Gauss C. F. Werke vol. III, 1866, p. 332.
- Gauss C. F. Werke. vol. III, 1866, pp. 361, 372, 375; vol. X, 1917, p. 173.
- Gauss C. F. Werke. vol. III, 1866, p. 491.
- Gauss C. F. Werke. vol. X, 1917, p. 251.
- David L. J. reine und angew. Math., 1909, vol. 135, p. 62; 1928, vol. 159, p. 154 Rend. Circolo mat. Palermo, 1913, v. 35, p. 82.
- Bela Barma. J. reine und angew. Math., 1934, vol. 172, p. 86; 1937. vol. 178. p. 129.