On the mean iteration

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

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

MSC:
Primary 30D05; Secondary 33A25

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

MathSciNet review:
968148

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Abstract | References | Similar Articles | Additional Information

Abstract: The iterative process

**[1]**J. Arazy, J. Claesson, S. Janson & J. Peetre,*Means and Their Iterations*, Proc. 19th Nordic Congr. Math. (J. R. Stefánson, ed.), Reykjavík, 1985. MR**828035 (87f:01012)****[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 & P. B. Borwein, "The arithmetic-geometric mean and fast computation of the elementary functions,"*SIAM Rev.*, v. 26, 1984, pp. 351-365. MR**750454 (86d:65029)****[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 & P. B. Borwein, "The way of all means,"*Amer. Math. Monthly*, v. 94, 1987, pp. 519-522. MR**1541118****[6]**R. P. Brent, "Fast multiple-precision evaluation of elementary functions,"*J. Assoc. Comput. Mach.*, v. 23, 1976, pp. 242-251. MR**0395314 (52:16111)****[7]**B. C. Carlson, "Algorithms involving arithmetic and geometric means,"*Amer. Math. Monthly*, v. 98, 1971, pp. 496-505. MR**0283246 (44:479)****[8]**D. H. Lehmer, "On the compounding of certain means,"*J. Math. Anal. Appl.*, v. 36, 1971, pp. 183-200. MR**0281696 (43:7411)****[9]**D. J. Newman, "A simplified version of the fast algorithms of Brent and Salamin,"*Math. Comp.*, v. 44, 1985, pp. 207-210. MR**771042 (86e:65030)****[10]**J. Peetre, "Generalizing the arithmetic-geometric mean--A hapless computer experiment," preprint.**[11]**E. Salamin, "Computation of using arithmetic-geometric mean,"*Math. Comp.*, v. 30, 1976, pp. 565-570. MR**0404124 (53:7928)**

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

Article copyright:
© Copyright 1989
American Mathematical Society