<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

Published Online: Dec 08, 2020

Page range: 53 - 65

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

Keywords
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

Published Online: Dec 08, 2020

Page range: 53 - 65

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

KeywordsNewton’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.

Keywords
Newton’s method, radius of convergence, local convergence