Newton's Method
Newton's Method, also known as the Newton-Raphson method, is an iterative numerical algorithm used to find successively better approximations to the roots (or zeroes) of a real-valued function. It uses the function's derivative to converge quadratically to a solution, making it efficient for solving equations where analytical solutions are difficult or impossible. This method is widely applied in optimization, engineering, physics, and machine learning for root-finding and minimization problems.
Developers should learn Newton's Method when working on problems involving numerical analysis, such as solving nonlinear equations, optimizing functions in machine learning (e.g., training neural networks), or implementing algorithms in scientific computing. It is particularly useful in scenarios where high precision is required and the function is differentiable, as it offers faster convergence compared to simpler methods like the bisection method. For example, it's used in computer graphics for ray tracing or in finance for calculating implied volatility.