On the mean iteration

Authors:
J. M. Borwein and P. B. Borwein

Journal:
Math. Comp. **53** (1989), 311-326

MSC:
Primary 30D05; Secondary 33A25

MathSciNet review:
968148

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Abstract | References | Similar Articles | Additional Information

Abstract: The iterative process

**[1]**Jonathan Arazy, Tomas Claesson, Svante Janson, and Jaak Peetre,*Means and their iterations*, Proceedings of the nineteenth Nordic congress of mathematicians (Reykjavík, 1984) Vísindafél. Ísl., XLIV, Icel. Math. Soc., Reykjavík, 1985, pp. 191–212. MR**828035****[2]**C. W. Borchardt,*Ueber das Arithmetisch-geometrische Mittel aus vier Elementen*, Berl. Monatsber., 1876, pp. 611-621. Werke, Berlin, 1888, pp. 329-338.**[3]**J. M. Borwein and P. B. Borwein,*The arithmetic-geometric mean and fast computation of elementary functions*, SIAM Rev.**26**(1984), no. 3, 351–366. MR**750454**, 10.1137/1026073**[4]**J. M. Borwein & P. B. Borwein,*Pi and the AGM--A Study in Analytic Number Theory and Computational Complexity*, Wiley, New York, 1987.**[5]**J. M. Borwein and P. B. Borwein,*Unsolved Problems: The Way of All Means*, Amer. Math. Monthly**94**(1987), no. 6, 519–522. MR**1541118**, 10.2307/2322842**[6]**Richard P. Brent,*Fast multiple-precision evaluation of elementary functions*, J. Assoc. Comput. Mach.**23**(1976), no. 2, 242–251. MR**0395314****[7]**B. C. Carlson,*Algorithms involving arithmetic and geometric means*, Amer. Math. Monthly**78**(1971), 496–505. MR**0283246****[8]**D. H. Lehmer,*On the compounding of certain means*, J. Math. Anal. Appl.**36**(1971), 183–200. MR**0281696****[9]**D. J. Newman,*A simplified version of the fast algorithms of Brent and Salamin*, Math. Comp.**44**(1985), no. 169, 207–210. MR**771042**, 10.1090/S0025-5718-1985-0771042-1**[10]**J. Peetre, "Generalizing the arithmetic-geometric mean--A hapless computer experiment," preprint.**[11]**Eugene Salamin,*Computation of 𝜋 using arithmetic-geometric mean*, Math. Comp.**30**(1976), no. 135, 565–570. MR**0404124**, 10.1090/S0025-5718-1976-0404124-9

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0968148-4

Article copyright:
© Copyright 1989
American Mathematical Society