Directional Secant-Type Methods for Solving Equations
A semilocal convergence analysis for directional Secant-type methods in multidimensional space is provided. Using weaker hypotheses than the ones exploited by An and Bai, we provide a semilocal convergence analysis with the following advantages: weaker convergence conditions, larger convergence domain, finer error estimates on the distances involved, and more precise information on the location of the solution. A numerical example, where our results apply to solve an equation but not the ones of An and Bai, is also provided. In a second example, we show how to implement the method.
directional secant-type method directional newton method nonlinear equations newtonkantorovich hypotheses lipschitz/center-lipschitz condition