Numerical Algorithms

, Volume 71, Issue 4, pp 933–951

# Semilocal convergence of an eighth-order method in Banach spaces and its computational efficiency

Original Paper

## Abstract

The aim of this paper is to study the semilocal convergence of the eighth-order iterative method by using the recurrence relations for solving nonlinear equations in Banach spaces. The existence and uniqueness theorem has been proved along with priori error bounds. We have also presented the comparative study of the computational efficiency in case of R m with some existing methods whose semilocal convergence analysis has been already discussed. Finally, numerical application on nonlinear integral equations is given to show our approach.

## Keywords

Nonlinear equation Banach space Recurrence relation Semilocal convergence Error bound Computational efficiency

## Mathematics Subject Classification (2010)

65H10 65J15 47J25

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