An improved semilocal convergence analysis for the midpoint method

Authors

  • Ioannis K. Argyros Cameron University, USA
  • Sanjay K. Khattri Department of Engineering, Stord Haugesund University College, Norway

DOI:

https://doi.org/10.33993/jnaat452-1104

Keywords:

midpoint method, semilocal convergence, majorizing sequence, Banach space, Frechet derivative
Abstract views: 202

Abstract

We expand the applicability of the midpoint method for approximating a locally unique solution of nonlinear equations in a Banach space setting. Our majorizing sequences are finer than the known results in scientific literature [1,3,4,5,6,7,8,9,10,11,19,20,21,23] and the convergence criteria can be weaker. Finally, numerical work is reported that compares favorably to the existing approaches in the literature [6, 8-16, 24-26,28]. 

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Author Biography

Ioannis K. Argyros, Cameron University, USA

Full tenured Professor of Mathematics.

References

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Published

2016-12-10

How to Cite

Argyros, I. K., & Khattri, S. K. (2016). An improved semilocal convergence analysis for the midpoint method. J. Numer. Anal. Approx. Theory, 45(2), 109–127. https://doi.org/10.33993/jnaat452-1104

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