Extending the applicability of Newton's and Secant methods under regular smoothness

Ioannis K. Argyros; Santhosh George; Shobha M. Erappa

doi:10.5269/bspm.42132

Ioannis K. Argyros Cameron University https://orcid.org/0000-0002-9189-9298
Santhosh George National Institute of Technology Karnataka https://orcid.org/0000-0002-3530-5539
Shobha M. Erappa Manipal Institute of Technology https://orcid.org/0000-0002-6523-0873

Resumo

The concept of regular smoothness has been shown to be an appropriate and powerfull tool for the convergence of iterative procedures converging to a locally unique solution of an operator equation in a Banach space setting. Motivated by earlier works, and optimization considerations, we present a tighter semi-local convergence analysis using our new idea of restricted convergence domains. Numerical examples complete this study.

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Biografia do Autor

Ioannis K. Argyros, Cameron University

Professor,
Department of Mathematics Sciences

Santhosh George, National Institute of Technology Karnataka

Professor,

Department of Mathematical and Computational Sciences

Shobha M. Erappa, Manipal Institute of Technology

Department of Mathematics

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