On the quadratic convergence of Newton's method under center-Lipschitz but not necessarily Lipschitz hypotheses

In: Mathematica Slovaca, vol. 63, no. 3

Ioannis K. Argyros - Saïd Hilout

Details:

Year, pages: 2013, 621 - 638

Keywords:

Newton's method, Banach space, majorizing sequences, Lipschitz/center-Lipschitz condition, local/semilocal convergence, radius of convergence, Kantorovich hypothesis

DOI: https://doi.org/10.2478/s12175-013-0123-4

About article:

We provide new local and semilocal convergence results for Newton's method in a Banach space. The sufficient convergence conditions do not include the Lipschitz constant usually associated with Newton's method. Numerical examples demonstrating the expansion of Newton's method are also provided in this study.

How to cite:

ISO 690:

Argyros, I., Hilout, S. 2013. On the quadratic convergence of Newton's method under center-Lipschitz but not necessarily Lipschitz hypotheses. In Mathematica Slovaca, vol. 63, no.3, pp. 621-638. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0123-4

APA:

Argyros, I., Hilout, S. (2013). On the quadratic convergence of Newton's method under center-Lipschitz but not necessarily Lipschitz hypotheses. Mathematica Slovaca, 63(3), 621-638. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0123-4

About edition: