A simplified version of the fast algorithms of Brent and Salamin
HTML articles powered by AMS MathViewer
- by D. J. Newman PDF
- Math. Comp. 44 (1985), 207-210 Request permission
Abstract:
We produce more elementary algorithms than those of Brent and Salamin for, respectively, evaluating ${e^x}$ and $\pi$. Although the Gauss arithmetic-geometric process still plays a central role, the elliptic function theory is now unnecessary.References
- Richard P. Brent, Fast multiple-precision evaluation of elementary functions, J. Assoc. Comput. Mach. 23 (1976), no. 2, 242–251. MR 395314, DOI 10.1145/321941.321944
- Richard P. Brent, Multiple-precision zero-finding methods and the complexity of elementary function evaluation, Analytic computational complexity (Proc. Sympos., Carnegie-Mellon Univ., Pittsburgh, Pa., 1975) Academic Press, New York, 1976, pp. 151–176. MR 0423869
- Eugene Salamin, Computation of $\pi$ using arithmetic-geometric mean, Math. Comp. 30 (1976), no. 135, 565–570. MR 404124, DOI 10.1090/S0025-5718-1976-0404124-9
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Math. Comp. 44 (1985), 207-210
- MSC: Primary 65D20
- DOI: https://doi.org/10.1090/S0025-5718-1985-0771042-1
- MathSciNet review: 771042