Newton-Kantorovich type theorem by using recurrence relations for a fifth-order method in Banach spaces

作者：Chen Liang^*

来源：Journal of Computational Analysis and Applications, 2014, 17(3): 486-497.

• Nonlinear equations
• Newton-Kantorovich type theorem
• Recurrence relations
• A priori error bounds

The Newton-Kantorovich type theorem of a fifth order Newton's method for solving nonlinear equations in Banach spaces is established by using recurrence relations in this paper, this theorem is proved under the assumption that the second Frechet derivative of F satisfies Lipschitz condition. Using recurrence relations, a priori error bounds are derived along with the domains of existence and uniqueness of the solutions. The R-order convergence of the method is five. Finally, a numerical example is worked out to demonstrate the efficacy of our approach.

• 出版日期2014-11
• 单位淮北师范大学