IMA Journal of Numerical Analysis · 2002 · 72 citations · 0 references
The use of majorizing sequences is the usual way to prove the convergence of Newton's method. An alternative technique to majorizing sequences is provided in this paper, in which three scalar sequences are used, so that the analysis of convergence is simplified when the traditional convergence condition is relaxed. An application to a nonlinear integral equation is also given, which is also solved and the solution approximated by a discretization process.