Semilocal Convergence fora Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces

[摘要] We study a modified Newton's method with fifth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations. The recurrence relations for the method are derived, and then an existence-uniqueness theorem is given to establish theR-order of the method to be five and a priori error bounds. Finally, a numerical application is presented to demonstrateour approach.

[学科分类] 应用数学