Stability Analysis of Jacobian-Free Newton’s Iterative Method - Abdolreza Amiri; Alicia Cordero; Mohammad Taghi Darvishi; Juan R. Torregrosa (Algorithms, 2019)
It is well known that scalar iterative methods with derivatives are highly more stable than their derivative-free partners, understanding the term stability as a measure of the wideness of the set of converging initial estimations. In multivariate case, multidimensional dynamical analysis allows us to afford this task and it is made on different Jacobian-free variants of Newton’s method, whose estimations of the Jacobian matrix have increasing order. The respective basins of attraction and the number of fixed and critical points give us valuable information in this sense.