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Convergence and Complexity of Newton Iteration for Operator Equations

Authors:

J. F. Traub,

H. WoźniakowskiAuthors Info & Claims

Journal of the ACM (JACM), Volume 26, Issue 2

Pages 250 - 258

https://doi.org/10.1145/322123.322130

Published: 01 April 1979 Publication History

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References

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DEN HEIJER, C Iterat~ve soluUon of nordmear equations by tmbeddmg methods Rep NW 32/76, Mathemausch Centrum, Amsterdam, Aug. 1976

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ORTEGA, J.M., AND RHEINBOLDT) W C lterattve Solutlon of Nonhnear Equattons m Several Variables Academic Press, New York, 1970.

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RALL, L B, Computattonai Solution of Nonhnear Operator Equations. Wiley, New York, 1969

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gALL, L.B. A note on the convergence of Newton's method. SIAM J Numer. Anal 11 (1974), 34--36.

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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

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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.

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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.

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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

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https://doi.org/10.4153/S000843952400016X
Argyros IGeorge SShakhno SRegmi SHavdiak MArgyros M(2024)Asymptotically Newton-Type Methods without Inverses for Solving EquationsMathematics10.3390/math1207106912:7(1069)Online publication date: 2-Apr-2024
https://doi.org/10.3390/math12071069
Argyros IGeorge SRegmi SArgyros C(2024)Hybrid Newton-like Inverse Free Algorithms for Solving Nonlinear EquationsAlgorithms10.3390/a1704015417:4(154)Online publication date: 10-Apr-2024
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Index Terms

Convergence and Complexity of Newton Iteration for Operator Equations
1. Mathematics of computing
  1. Discrete mathematics
  2. Mathematical analysis
    1. Nonlinear equations

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Published In

Journal of the ACM Volume 26, Issue 2

April 1979

205 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/322123

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 April 1979

Published in JACM Volume 26, Issue 2

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Argyros IGeorge S(2024)On the complexity of extending the convergence domain of Newton’s method under the weak majorant conditionCanadian Mathematical Bulletin10.4153/S000843952400016X(1-15)Online publication date: 1-Mar-2024
https://doi.org/10.4153/S000843952400016X
Argyros IGeorge SShakhno SRegmi SHavdiak MArgyros M(2024)Asymptotically Newton-Type Methods without Inverses for Solving EquationsMathematics10.3390/math1207106912:7(1069)Online publication date: 2-Apr-2024
https://doi.org/10.3390/math12071069
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