On Newton's method for subanalytic equations

Ioannis K. Argyros; Santhosh George

doi:10.33993/jnaat461-1132

Authors

Ioannis K. Argyros Cameron University, Department of Mathematicsal Sciences, Lawton, USA
Santhosh George National Institute of Technology Karnataka, Department of Mathematical and Computational Sciences, India

DOI:

https://doi.org/10.33993/jnaat461-1132

Keywords:

Newton's methods, convergence ball, local-semilocal convergence, subanalytic functions

Abstract views: 382

Abstract

We present local and semilocal convergence results for Newton’s method in order to approximate solutions of subanalytic equations. The local convergence results are given under weaker conditions than in earlier studies such as [9], [10], [14], [15], [24], [25], [26], resulting to a larger convergence ball and a smaller ratio of convergence. In the semilocal convergence case contravariant conditions not used before are employed to show the convergence of Newton’s method. Numerical examples illustrating the advantages of our approach are also presented in this study.

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Author Biography

Ioannis K. Argyros, Cameron University, Department of Mathematicsal Sciences, Lawton, USA

Full tenured Professor of Mathematics.

References

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