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.

The Babylonian square root and bisection

The Babylonian square root and bisection

Newton-Raphson’s method: tangent lines and quadratic convergence

Newton-Raphson's method: tangent lines and quadratic convergence

Halley’s method: cubic convergence

Halley's method: cubic convergence

Aitken’s delta-squared process and Steffensen’s method

Aitken's delta-squared process and Steffensen's method