Weak convergence conditions for the Newton’s method in Banach space using general majorizing sequences

摘要

Using the majorizing principle, we develop sufficient convergence conditions for the semilocal convergence of Newton’s method in a Banach space setting. The involved majorizing sequences are very general and, as special cases, include most relevant sequences from the published literature. Our convergence conditions can be weaker and our error analysis can be finer than before.