name

Brady Elster

Author

Root-Finding Problems

f(x)=0\begin{aligned} f(x) = 0 \end{aligned}

Bisection Method

Regula Falsi (False Position)

Newton's Method

Order of Convergence

Let rr be the root of our function and xnx_{n} be the nn-th approximation ot the root. Then we define the error as

ϵn=r−xn. \begin{equation} \epsilon_{n} = r - x_{n}. \end{equation}

For large nn we assume the approximate relatonship

∣ϵn+1∣=k∣ϵn∣p \begin{equation} |\epsilon_{n+1}| = k |\epsilon_{n}|^{p} \end{equation}
CC BY-SA 4.0 Brady Elster. Last modified: August 17, 2025. Website built with Franklin.jl and the Julia programming language.