MATLAB Implementation of Newton's Iteration Method with Code Examples

The Newton-Raphson method implementation in MATLAB serves as an effective computational tool particularly beneficial for beginners advancing their numerical methods skills. This implementation typically involves defining the target function and its derivative, then applying the iterative formula x_{n+1} = x_n - f(x_n)/f'(x_n) through a loop structure with convergence criteria. Through hands-on experimentation, students gain deeper understanding of root-finding algorithms, convergence behavior, and error analysis. The MATLAB environment provides intuitive programming syntax for implementing the core algorithm using function handles, where key functions like feval or direct function calls calculate iterations. The implementation often includes features such as maximum iteration limits, tolerance settings for convergence checks, and graphical visualization of convergence progress. MATLAB's user-friendly interface and built-in plotting capabilities enable learners to visualize iteration steps and understand the method's geometric interpretation. This practical approach helps students quickly grasp numerical analysis concepts while developing debugging skills through trial-and-error experimentation. The method's simplicity and computational efficiency make it a popular educational tool among both instructors and engineering practitioners for solving nonlinear equations.