A QUADRATICALLY CONVERGENT NEWTON-LIKE METHOD BASED UPON GAUSSIAN ELIMINATION

Author presents an iterative method for the numerical solution of a real-valued twice continuously differentiable system of N nonlinear equations in N unknowns. The method is a variation of Newton's method incorporating Gaussian elimination in such a way that the most recent information is always used at each step of the algorithm. After specifying the method interms of an iteration function, it is proved that the iteration converges locally and that the convergence is quadratic in nature. Computer results are given and a comparison is made with Newton'smethod; these results illustrate the effectiveness of the method for nonlinear systems containing linear or mildly nonlinear equations.