Extending the solvability of equations using secant-type methods in Banach space

Ioannis K. Argyros; Santhosh George

doi:10.33993/jnaat502-1134

Authors

Ioannis K. Argyros Cameron University, USA
Santhosh George Department of Mathematical and Computational Sciences, NIT Karnataka, India

DOI:

https://doi.org/10.33993/jnaat502-1134

Keywords:

nonlinear equations in Banach space, secant method, Secant-type method, Semi-local convergence, restricted convergence region, Lipschitz conditions

Abstract views: 233

Abstract

We extend the solvability of equations dened on a Banach space using numerically ecient secant-type methods. The convergence domain of these methods is enlarged using our new idea of restricted convergence region. By using this approach, we obtain a more precise location where the iterates lie than in earlier studies leading to tighter Lipschitz constants. This way the semi-local convergence produces weaker sucient convergence criteria and tighter error bounds than in earlier works. These improvements are also obtained under the same computational eort, since the new Lipschitz constants are special cases of the old ones.

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Author Biography

Ioannis K. Argyros, Cameron University, USA

Full tenured Professor of Mathematics.

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