An improved convergence and complexity analysis for the interpolatory Newton method

Ioannis K. Argyros

doi:10.4067/S0719-06462010000100013

An improved convergence and complexity analysis for the interpolatory Newton method

Authors

Ioannis K. Argyros Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA.

DOI:

https://doi.org/10.4067/S0719-06462010000100013

Keywords:

Newton‘s method, local convergence, Banach space, interpolatory Newton method, complexity, radius of convergence

Abstract

We provide an improved compared to [5]–[7] local convergence analysis and complexity for the interpolatory Newton method for solving equations in a Banach space setting. The results are obtained using more precise error bounds than before [5]–[7] and the same hypotheses/computational cost.