# Bisection & Root-Finding Methods (C++) ## Introduction Bisection is a robust root-finding technique for continuous functions where the function changes sign over an interval `[a,b]`. It repeatedly halves the interval until the root is approximated to desired tolerance. ## Algorithm - Ensure `f(a)` and `f(b)` have opposite signs. - Compute midpoint `m=(a+b)/2`. If `f(m)` close to 0 or interval small, stop; otherwise replace interval `[a,m]` or `[m,b]` depending on sign and repeat. ## Complexity - Converges linearly; number of iterations ≈ `log2((b-a)/tol)`. ## Notes on repo file The provided file `bisection.cpp` uses a variant formula (looks like secant/newton hybrid). For standard bisection, prefer midpoint selection. If using derivative-based methods, validate monotonicity and derivative availability. ## Practical tips - Bisection is guaranteed to converge but slowly. Use Newton or secant for faster convergence if derivative (or good guesses) is available. - Always guard against dividing by zero. ## Source `https://github.com/mashrur-rahman-fahim/algorithm/blob/main/bisection.cpp`.