A convergence analysis of an iterative algorithm of order \(1.839\ldots\) under weak assumptions

Ioannis K. Argyros

doi:10.33993/jnaat322-741

Authors

Ioannis K. Argyros Cameron University, Lawton, USA

DOI:

https://doi.org/10.33993/jnaat322-741

Keywords:

Banach space, majorizing sequence, Halley method, Euler-Chebyshev method, divided differences of order one and two, Fréchet-derivative, \(R\)-order of convergence, convergence radius

Abstract views: 235

Abstract

We provide new and weaker sufficient local and semilocal conditions for the convergence of a certain iterative method of order 1.839\(\ldots\) to a solution of an equation in a Banach space. The new idea is to use center-Lipschitz/Lipschitz conditions instead of just Lipschitz conditions on the divided differences of the operator involved. This way we obtain finer error bounds and a better information on the location of the solution under weaker assumptions than before.

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References

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