Math — Newton-Raphson Method
Iterative root finding and its quadratic convergence.
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x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}
\varepsilon_{n+1} \approx \frac{f''(x^*)}{2f'(x^*)}\,\varepsilon_n^2
\text{Secant: } x_{n+1} = x_n - f(x_n)\frac{x_n - x_{n-1}}{f(x_n) - f(x_{n-1})}