Approximating solutions of equations using Newton's method with a modified Newton's method iterate as a starting point

Ioannis Argyros

doi:10.33993/jnaat362-862

Authors

Ioannis Argyros Cameron University, USA

DOI:

https://doi.org/10.33993/jnaat362-862

Keywords:

Banach space, Newton-Kantorovich method, radius of convergence, Fréchet-derivative, Banach lemma on invertible operators

Abstract views: 379

Abstract

In this study we are concerned with the problem of approximating a locally unique solution of an equation in a Banach space setting using Newton's and modified Newton's methods. We provide weaker convergence conditions for both methods than before [6]-[8]. Then, we combine Newton's with the modified Newton's method to approximate locally unique solutions of operator equations in a Banach space setting. Finer error estimates, a larger convergence domain, and a more precise information on the location of the solution are obtained under the same or weaker hypotheses than before [6]-[8]. Numerical examples are also provided.

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References

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