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Keywords:
Banach space; Newton's method; local convergence; radius of convergence
Banach space; Newton's method; local convergence; radius of convergence
Summary:
We present a local convergence analysis of a one parameter Jarratt-type method. We use this method to approximate a solution of an equation in a Banach space setting. The semilocal convergence of this method was recently carried out in earlier studies under stronger hypotheses. Numerical examples are given where earlier results such as in [Ezquerro J.A., Hernández M.A., {New iterations of $R$-order four with reduced computational cost}, BIT Numer. Math. {49} (2009), 325--342] cannot be used to solve equations but our results can be applied.
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