Applying twice an idea of Hernández and Rubio (2002) for constructing a one-parameter family of secant-like methods, we define a two-parameter family of secant-like methods for solving nonlinear systems of equations. We analyze the efficiency of this new family and conclude that the Kurchatov method, which is one member of the family, is the most efficient. We illustrate this with Troesch’s problem.
"A new class of secant-like methods for solving nonlinear systems of equations." Commun. Appl. Math. Comput. Sci. 9 (2) 201 - 213, 2014. https://doi.org/10.2140/camcos.2014.9.201