A new Newton’s method with diagonal Jacobian approximation for solving systems of nonlinear equations

Abstract

The most prominent method for solving systems of nonlinear equations is the Newton’s method, which required computation of Jacobian matrix and solving system of n -linear equations in each of the iterations. Jacobian mostly is computationally expensive and requires evaluation (storage) of fully populated matrix of dimensionnn×. This storage qualification becomes impractical when n becomes large. The method proposed in this paper aims at reducing the storage requirement and computational cost of the Jacobian as well as CPU time. This is made possible by approximating the Jacobian into a diagonal matrix. The method is suitable for solving small, medium and large scale nonlinear systems with dense or sparse Jacobian. The convergence of the method has been proved. Numerical experiments are carried out which shows that, the proposed method is very encouraging.