Convergence and Complexity of Newton Iteration for Operator Equations

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Convergence and Complexity of Newton Iteration for Operator Equations

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Journal of the ACM (JACM) archive
Volume 26 , Issue 2 (April 1979) table of contents

Pages: 250 - 258

Year of Publication: 1979

ISSN:0004-5411

Authors

J. F. Traub	Department of Computer Science, Carnegie-Mellon University, Pittsburgh, PA
H. Woźniakowski	Department of Computer Science, Carnegie-Mellon University, Pittsburgh, PA

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 9, Downloads (12 Months): 56, Citation Count: 5

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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	DEN HEIJER, C Iterat~ve soluUon of nordmear equations by tmbeddmg methods Rep NW 32/76, Mathemausch Centrum, Amsterdam, Aug. 1976
	2	GRAGG, W B, AND TAPIA, R A Optn'nal error bounds for the Newton-Kantorovich theorem SIAM J. Numer. Anal. 11 (1974), 10-13
	3	KANTOROVICH, UV. Funct,onal analysis and apphed mathematics Uspeht Mat Nauk 3 (1948), 89-185 (Russian) Tr by C.D. Benster, Rep. No 1509, Nat Bur Stand., Washington, D.C., 1952
	4	James M. Ortega , Werner C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2000
	5	RALL, L B, Computattonai Solution of Nonhnear Operator Equations. Wiley, New York, 1969
	6	gALL, L.B. A note on the convergence of Newton's method. SIAM J Numer. Anal 11 (1974), 34--36.
	7	RHEINBOLDT, W.C An adaptive continuation process for solving systems of nonlinear equaUons. Tech Rep TR-393, U. of Maryland, College Park, Md., July 1975
	8	TRAUB, J.F., AND WOZNIAKOWSKI, H. Strict lower and upper bounds on lterative computational complex,ty. In Analytic Computattonal Complextty, J F. Traub, Ed., Academ,c Press, New York, 1976, pp 15-34.
	9	T~uB, J.F., AND WOZNIAKOWSKI, H Opttmal radius of convergence of interpolatory lterattons for operator equations. Rep., Dept. Comptr. Sci, Carnegie-Mellon U., Ptttsburgh, Pa., 1976 To appear m Aequattones Mathematicae.
	10	TRAUB, J F, AND WOZNIAKOWSKI, H. Convergence and complexity of mterpolatory-Newton ~teratlon m a Banach space Rep, Dept. Comptr Sci, Carnegie-Mellon U, Pittsburgh, Pa, 1977

CITED BY 5

	Jinhai Chen , Weiguo Li, Convergence behaviour of inexact Newton methods under weak Lipschitz condition, Journal of Computational and Applied Mathematics, v.191 n.1, p.143-164, 15 June 2006
	Ren Hongmin , Wu Qingbiao, The convergence ball of the Secant method under Hölder continuous divided differences, Journal of Computational and Applied Mathematics, v.194 n.2, p.284-293, 1 October 2006
	Nuchun Hu , Weiping Shen , Chong Li, Kantorovich's type theorems for systems of equations with constant rank derivatives, Journal of Computational and Applied Mathematics, v.219 n.1, p.110-122, September, 2008
	Ioannis K. Argyros, Improved convergence and complexity analysis of Newton's method for solving equations, International Journal of Computer Mathematics, v.84 n.1, p.67-73, January 2007
	Petko D. Proinov, General local convergence theory for a class of iterative processes and its applications to Newton's method, Journal of Complexity, v.25 n.1, p.38-62, February, 2009