LOCAL CONVERGENCE OF THE NEWTON’S METHOD IN TWO STEP NILPOTENT LIE GROUPS
In this paper, we consider N, a simply connected two-step nilpotent Lie group with L(N), its
corresponding (two-step nilpotent) Lie algebra, and we study Newton’s method for solving the equation
f (x) = 0, where f is a mapping from N to L(N). 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 f .
Some applications to special cases including Kantorovich’s condition and g-condition are provided. The
determination of an approximate zero point of an analytic mapping is also presented.
We classify irreducible homogeneous almost Hermite-Lorentz spaces of complex dimension 3, and prove in particular they are geodesically complete.
In this paper, we consider N, a simply connected two-step nilpotent Lie group with L(N), its
corresponding (two-step nilpotent) Lie algebra, and we study Newton’s method for solving the…
Abstract. A bounded operator S on a Hilbert space is hyponormal if S*S-SS* is positive. In this work we find necessary conditions for the hyponormality of the Toeplitz operaor T_f+g^- on the…