👉 Retreat math, often used in the context of iterative methods for solving equations, involves a process where an initial guess is repeatedly refined through a mathematical operation until a desired level of accuracy or a stopping criterion is met. The core idea is to start with an initial guess \( x_0 \) and iteratively apply a function \( f(x) \) to produce a sequence of approximations: \( x_{n+1} = f(x_n) \). Each step aims to converge towards a root or solution of the equation \( f(x) = 0 \). The choice of function and the stopping criteria (e.g., a tolerance on the change in \( x \) or the function value) determine how accurately the solution is refined. This method is widely used in numerical analysis and computer science for solving nonlinear equations, optimization problems, and more.
