Root finding#
The Babylonian square-root rule and bisection, Newton-Raphson’s tangent iteration, Halley’s cubically convergent method, and Aitken/Steffensen acceleration, each with its empirical convergence order measured; then Newton’s method for systems of equations and Broyden’s quasi-Newton method, which saves the Jacobian evaluations.
An animation runs Newton against bisection on the graph of \(f\).
Newton-Raphson’s method: tangent lines and quadratic convergence
Newton-Raphson's method: tangent lines and quadratic convergence
Aitken’s delta-squared process and Steffensen’s method
Aitken's delta-squared process and Steffensen's method
Animated: Newton’s tangents against bisection’s halving
Animated: Newton's tangents against bisection's halving