num::bisection

Defined in header <roots/roots.hpp>

template <typename Float = double, bracketable_function<Float> Func = scalar_fn>
root_result<Float> bisection(Func &&f, Float a, Float b, Float tol = Float{1e-10},
                             idx max_iter = 1000);

Bisection method for finding a root on a bracketing interval \([a, b]\) where \(f(a) f(b) \le 0\).

Guaranteed linear convergence halving the interval width at each step: \(|x_k - x^*| \le \frac{b-a}{2^k}\).

Template parameters

• Float: scalar floating-point type (double, float).
• Func: Function callable Float(Float x).

Parameters

• f: Target continuous function.
• a: Left interval endpoint.
• b: Right interval endpoint.
• tol: Error tolerance on interval radius and residual \(|f(x)|\) (default: 1e-10).
• max_iter: Maximum iterations (default: 1000).

Return value

root_result<Float> with root approximation, iteration count, final residual, and convergence status.

Exceptions

• std::invalid_argument: If \(f(a)\) and \(f(b)\) have the same sign.

See also

brent, newton, secant