Answer to Question #140446 in Electrical Engineering for Daksh

Question

Discuss the order of the convergence of the Newton's method for nonlinear equation
f (x) = 0

Answer 1

System of nonlinear equations arises in many parts of the engineering, physics and biology applications. In most cases, the system arisen almost impossible to be solved analytically, hence numerical analysis become the fashion. For many years, Newton's method seems to be the best method in solving the problems but some issues came out afterwards. For example, the Jacobian matrix, J that need to be supplied in each iteration required a lot of calculation works and consumed a lot of time. In this project, a new algorithm called Quasi-Newton method which used a matrix B as an approximation for the Jacobian matrix has been used in solving system of nonlinear equations. The method shown less computational works or higher time efficiency compared to Newton's method.