Abstract. In this paper, we consider , a simply connected two-step nilpotent Lie group with , its corresponding (two-step nilpotent) Lie algebra, and we study Newton’s method for solving the equation , where is a mapping. Under certain generalized Lipschitz condition, we obtain the convergence radius of Newton’s method and the estimation of the uniqueness ball of the zero point of . Some applications to special cases including Kantorovich’s condition and -condition are provided. The determination of an approximate zero point of an analytic mapping is also presented.
How to Cite this Article:
B. Dali, M. Guediri, Local convergence of the Newton’s method in two step nilpotent Lie groups, J. Nonlinear Var. Anal. 6 (2022), 199-212.
