Sufficient conditions for constructing methods faster than Newton's

摘要

In this study we use inexact Newton-like methods to approximate a locally unique solution of a nonlinear operator equation in a Banach space. Using the majorant method and Newton Kantorovich-type hypotheses we provide sufficient convergence conditions and an error analysis for our method. Our method is also shown under very natural assumptions to be faster than Newton's under the same computational cost. Finally we apply our results to solve nonlinear integral equations appearing in radiative transfer in connection with the problem of determination of the angular distribution of the radiant-flux emerging from a plane radiation field.