Error Bounds for Newton-Like Methods Under Kantorovich Type Assumptions

摘要

To find sharper error bounds for iterative solutions of nonlinear equations is one of the important subjects in numerical analysis. This paper gives a method to derive new a posteriori error bounds for Newton-like methods in a Banach space under Kantorovich type assumptions. The bounds found are sharper than those of Miel and include those recently obtained by Moret. The applicability of the author's method is studied for other types of iterations. Various error bounds for the Newton method under the Kantorovich assumptions are surveyed in the Appendix.