An Algorithm for Deciding the Convergence of the Rational Iteration xn+1= f(xn)

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An Algorithm for Deciding the Convergence of the Rational Iteration xn+1= f(xn)

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 3 , Issue 3 (September 1977) table of contents

Pages: 272 - 278

Year of Publication: 1977

ISSN:0098-3500

Author

Richard J. Fateman

Computer Science Division, Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA

Publisher

ACM New York, NY, USA

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	COLLINS, G.E., AND HEINDEL, L.E. The SAC-I polynomial real-zero system. Comptr. Ctr., Tech. Rep. No. 18, U. of Wisconsin, Madison, Wis., Aug. 1970.
	2	George E. Collins , Alkiviadis G. Akritas, Polynomial real root isolation using Descarte's rule of signs, Proceedings of the third ACM symposium on Symbolic and algebraic computation, p.272-275, August 10-12, 1976, Yorktown Heights, New York, United States [doi>10.1145/800205.806346]
	3	George E. Collins , Rüdiger Loos, Polynomial real root isolation by differentiation, Proceedings of the third ACM symposium on Symbolic and algebraic computation, p.15-25, August 10-12, 1976, Yorktown Heights, New York, United States [doi>10.1145/800205.806319]
	4	FATEMAN, R.J. An improved algorithm for the isolation of polynomial real zeros. Proc. 1977 MACSYMA Users' Conf., Berkeley, Calif., July 27, 1977.
	5	Lee E. Heindel, Integer Arithmetic Algorithms for Polynomial Real Zero Determination, Journal of the ACM (JACM), v.18 n.4, p.533-548, Oct. 1971 [doi>10.1145/321662.321667]
	6	KAHAN, W. No period two implies convergence, or why use tangents when secants will do. U. of California, Berkeley, Cahf., 1976; to appear in SIAM Rev.
	7	Mathlab Group. MACSYMA Reference Manual. Lab. Comptr. Sci., M.I.T., Cambridge. Mass, Nov. 1975.
	8	SARKOVSKII, A.N. On cycles and the structures of a continous mapping. Math. Rev. 3~ (1966), 4213; Ukrazn. Mat. Z 17, 3 (1965), 104-131 (Russian).
	9	P. Verbaeten, Computing real zeros of polynomials with SAC-1, ACM SIGSAM Bulletin, v.9 n.2, p.8-10, May 1975 [doi>10.1145/1088301.1088304]