<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the present paper, we consider a construction proposed in Xiao and Yin (2016) to improve the order of convergence of the method from <italic>p</italic> to <italic>p</italic> + 2<italic>m</italic> under weaker assumptions. Using the idea of restricted convergence domains we extend the applicability of the method considered by Xiao and Yin (2016). Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.</p></abstract>

In the present paper, we consider a construction proposed in Xiao and Yin (2016) to improve the order of convergence of the method from p to p + 2m under weaker assumptions. Using the idea of restricted convergence domains we extend the applicability of the method considered by Xiao and Yin (2016). Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.

Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions

Department of Mathematical and Computational Sciences

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In the present paper, we consider a construction proposed in Xiao and Yin (2016) to improve the order of convergence of the method from p to p + 2m under...

Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions

Publié en ligne: 08 déc. 2020

Pages: 53 - 65

DOI: https://doi.org/10.2478/awutm-2019-0006

Mots clés
Newton’s method, radius of convergence, local convergence

© 2019 Ioannis K. Argyros et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions

Publié en ligne: 08 déc. 2020

Pages: 53 - 65

DOI: https://doi.org/10.2478/awutm-2019-0006

Mots clésNewton’s method, radius of convergence, local convergence

© 2019 Ioannis K. Argyros et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Newton’s method, radius of convergence, local convergence