Orthogonalized steepest descent method for solving nonlinear equations

This paper describes a novel algorithm based on Steepest Descent Method (SDM) for solving a system of nonlinear algebraic equations. First, we compare SDM with Newton-Raphson Method (NRM) and propose a novel technique which is derived from the equivalent property between them. The proposed method is an efficient algorithm which not only can overcome drawbacks of NRM but also can exploit the convergence speed of NRM. We refer to this technique as orthogonalized Steepest Descent Method. We demonstrate the validity of the proposed technique for several nonlinear equations and Hopfield neural network analysis