Local convergence of a one parameter fourth-order Jarratt-type metho¨d in Banach spaces

Commentationes mathematicae Universitatis Carolinae

I. K. Argyros¹ 

关键词: Banach space;    Newton's method;    local convergence;    radius of convergence;   

DOI  :  10.14712/1213-7243.2015.171

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

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.

【 授权许可】

CC BY