ON THE CONVERGENCE OF SOME PROJECTION METHODS AND INEXACT NEWTON-LIKE ITERATIONS

Main Article Content

IOANNIS K. ARGYROS

Abstract




We provide a general theorem for the convergence of some projection methods for inexact Newton-like iterations under Yamamoto-type assumptions. Our results extend and improve several situations already appeared in the literature.




Article Details

How to Cite
ARGYROS, I. K. (1994). ON THE CONVERGENCE OF SOME PROJECTION METHODS AND INEXACT NEWTON-LIKE ITERATIONS. Tamkang Journal of Mathematics, 25(4), 335–341. https://doi.org/10.5556/j.tkjm.25.1994.4462
Section
Papers

References

P. T . Brown, "A local convergence theory for inexact-Newton finite-difference projection methods," SIAM J. Numer. Anal., 24, (1987), 407-437.

X. Chen, T. Yamamoto, "Convergence domains of certain iterative methods for solving nonlinear equations," Numer. Funct. Anal. and Optimiz., IO, (1 and 2), (1989), 37-48.

R. S. Dembo, S. C. Eisenhart, and T. Steihaug, "Inexact Newton methods," SIAM J. Numer. Anal., 19, (1982), 400-408.

M. A. Krasnosel'skii, and Y. B. Rutickii, "Some approximate methods of solving nonlinear equations based on linearization," Soviet Math. Dokl., 2, (1961), 1542-1546.

I. Moret, "A Kantorovich-type theorem for inexact Newton methods," Numer. Funct. Anal. and Optimiz., 10, (3 and 4), (1989), 351-365.

F. A. Potra, and V. Ptak, Nondiscrete induction and iterative processes., Pitman Advanced Pub- lishing Program, London, 1984.

A. H. Sherman, "On Newton-iterative methods for the solution of systems of equations," SIAM J. Numer. Anal., 15, (1978), 755-771.

P. P. Zabrejko, and D. F. Nguen, "The majorant method in the theory of Newton-Kantorovich approximations and the Ptak error estimates," Numer. Funct. Anal. and Optimiz., 9, (1987), 671- 684 .

T. Yamamoto, "A note on a posterior error bound of Zabrejko and Nguen for Zincenko's iteration," Numer. Funct. Anal. and Optimiz., 9, (1987), 987-994.

T. J. Ypma, "Local convergence of inexact Newton methods," SIAM J. Numer. Anal., 21, (1984), 583-590.

Most read articles by the same author(s)

1 2 > >>