Relations Between Forcing Sequences and Inexact Newton Iterates in Banach Space

@article{Argyros1999RelationsBF,
  title={Relations Between Forcing Sequences and Inexact Newton Iterates in Banach Space},
  author={Ioannis K. Argyros},
  journal={Computing},
  year={1999},
  volume={63},
  pages={131-144}
}
We use inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Solving a nonlinear equation using Newton iterates at each stage is very expensive in general. That is why we consider inexact Newton methods, where the Newton equations are solved only approximately and in some unspecified manner. In the elegant paper [6] natural assumptions under which the forcing sequence is uniformly less than one were given based on the first-Fréchet derivative of the… CONTINUE READING

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 12 references

Inexact Newton methods

  • R. S. Dembo, S. C. Eisenstat, T. Steihaug
  • SIAM J. Numer. Anal. 19,
  • 1982
Highly Influential
8 Excerpts

The theory and application of iteration methods. Florida: CRC

  • I. K. Argyros, F. Szidarovszky
  • 1993
Highly Influential
5 Excerpts

Functional analysis

  • L. V. Kantorovich, G. P. Akilov
  • 1982
Highly Influential
5 Excerpts

A new semilocal convergence theorem for Newton ' s methods

  • J. M. Gutierez
  • Comput . Appl . Math .
  • 1998

Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton’s method

  • I. K. Argyros
  • Southwest J. Pure Appl. Math. 1,
  • 1998
1 Excerpt

A new semilocal convergence theorem for Newton’s method

  • J. M. Gutierez
  • J. Comput. Appl. Math. 79,
  • 1997
2 Excerpts

Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton ' s method , Southwest Journal of Pure Appl

  • I. K. Argyros
  • Math .
  • 1991

On the convergence of some projection methods with perturbation

  • I. K. Argyros
  • J. Comput. Appl. Math. 36,
  • 1991
1 Excerpt

On Q-order and R-order of convergence

  • F. A. Potra
  • SIAM J. Optimiz. Th. Appl. 63,
  • 1989
1 Excerpt

Similar Papers

Loading similar papers…