Bisection Method for Solving Nonlinear Equations | Root finding | Interval Halving скачать в хорошем качестве

Bisection Method for Solving Nonlinear Equations | Root finding | Interval Halving

Bisection Method for Solving Nonlinear Equations The Bisection Method is a simple iterative numerical technique used to find the root of a nonlinear equation within a specified interval. The method involves the following steps: 1. Initialization: Start with an interval [a, b] such that the function has opposite signs at the endpoints, i.e., f(a) * f(b) less than 0, indicating that a root lies within the interval. 2. Iteration: Divide the interval in half and evaluate the function at the midpoint, c = (a + b) / 2. If f(c) is very close to zero, then c is an approximate root, and the process can be terminated. If f(c) has the same sign as f(a), replace a with c. Otherwise, replace b with c. Repeat the process until the interval becomes sufficiently small or a predefined number of iterations is reached. 3. Convergence Criteria: The method typically terminates when the interval becomes sufficiently small or when the function value at the midpoint is close to zero. 4. Termination: The final interval [a, b] or the last computed midpoint c provides an approximation to the root of the nonlinear equation. The Bisection Method is straightforward and guaranteed to converge when the initial conditions are met. However, it may converge slowly, and other methods like Newton's method are often preferred for faster convergence in practice.