A Newton-like method for nonlinear system of equations

Tanabe (1988) proposed a variation of the classical Newton method for solving nonlinear systems of equations, the so-called Centered Newton method. His idea was based on a deviation of the Newton direction towards a variety called “Central Variety”. In this paper we prove that the Centered Newton method is locally convergent and we present a globally convergent method based on the centered direction used by Tanabe. We show the effectiveness of our proposal for solving nonlinear system of equations and compare with the Newton method with line search.