A semilocal convergence analysis for the method of tangent parabolas

Ioannis K. Argyros

doi:10.33993/jnaat341-786

Authors

Ioannis K. Argyros Cameron of University, Lawton, USA

DOI:

https://doi.org/10.33993/jnaat341-786

Keywords:

Banach space, tangent parabola, Euler-Chebyshev method, majorizing sequence, Fréchet-derivative, Lipschitz-center conditions

Abstract views: 224

Abstract

We present a semilocal convergence analysis for the method of tangent parabolas (Euler-Chebyshev) using a combination of Lipschitz and center Lipschitz conditions on the Fréchet derivatives involved. This way we produce a majorizing sequence which converges under weaker conditions than before. The error bounds obtained are more precise and the information of the location of the solution better than in earlier results.

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References

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