The Convergence Ball of Newton's Method and the Uniqueness Ball of Equations under Hölder-Type Continuous Derivatives

Computers and Mathematics with Applications

Volumn 47, Issue 2-3, 2004, Pages 247-251

  Huang, Zhengda ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

Convergence ball; Estimate of radius; Newton's method; Uniqueness ball

Indexed keywords

ALGORITHMS; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; THEOREM PROVING;

CONVERGENCE BALL; ESTIMATE OF RADIUS; NEWTON'S METHOD; UNIQUENESS BALL;

CONVERGENCE OF NUMERICAL METHODS;

EID: 1242329958     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0898-1221(04)90021-1     Document Type: Article

References (12)

1. J.F. Traub and H. Wozniakowski, Convergence and complexity of Newton iteration for operator equation, J. Assoc. Comput. Mech. 26, 250-258, (1979).
2. X. Wang, The convergence on Newton's method (in Chinese), Kexue Tongbao A Special Issue of Mathematics, Physics, & Chemistry 25, 36-37, (1980).
3. S. Smale, The Merging of Disciplines: New Directions in Pure, Applied, and Computational Mathematics, (Edited by R.E. Ewing, K.I. Grosa and C.F. Martin), pp. 185-196, Springer-Verlag, (1986).
4. X. Wang and D. Han, Criterion α and Newton's method in the weak conditions (in Chinese), Math. Numer. Sinica 19, 103-112, (1997).
5. X. Wang, Convergence of Newton's method and uniqueness of the solution of equations in Banach space, IMA J. Numer. Anal. 20, 123-134, (2000).
6. X. Wang and C. Li, Local and global behavior for algorithm for solving equations, Chinese Sci. Bull. 46, 444-448, (2001).
7. I.K. Argyros, On Newton's method under mild differentiability conditions and applications, Appl. Math. Comput. 102, 177-183, (1999).
8. I.K. Argyros, A convergence analysis for Newton-like methods in Banach space under weak hypotheses and applications, Tamkang J. Math. 30, 255-263, (1999).
9. H.T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover, New York, (1962).
10. M.A. Hernández, Relaxing convergence conditions for Newton's method, J. Math. Anal. App. 249, 463-475, (2000).
11. J. Rokne, Newton's method under mild differentiability conditions with error analysis, Numer. Math. 18, 401-412, (1972).
12. L.V. Kantorovich and G.P. Akilov, Functional Analysis, Pergamon, Oxford, (1982).