Abstract: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., Hern\'andez M.A., {\it New iterations of $R$-order four with reduced computational cost\/}, BIT Numer. Math. {\bf 49} (2009), 325--342] cannot be used to solve equations but our results can be applied.
Keywords: Banach space; Newton's method; local convergence; radius of convergence
DOI: DOI 10.14712/1213-7243.2015.171
AMS Subject Classification: 65D10 65D99