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Bisection Method

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Finds x such that f(x)=0 using bisection. Enter a and b such that f(a) and f(b) have opposite signs.
Although the bisection method converges slowly, it reliably approaches the solution.
It is suitable for finding initial values for the Newton method or the Halley method, which converge quickly.
f(x)
a
,
bChoose a and b such that
f(a)f(b)≦0
n
Maximum number of iterations
\(\normalsize Bisection\ method\\ (1)\ initial\ value a_0,\ b_0\hspace{20px}f(a_0)f(b_0)\le0\\ (2)\ x_n={\large\frac{a_n+b_n}{2}}\\ \hspace{25px}f(x_n)\le\varepsilon\ \Rightarrow\ answer=x_n\\ \hspace{25px} a_{n+1}=x_n,\ b_{n+1}=b_n\hspace{20px}f(a_n)f(x_n)\ge0\\ \hspace{25px} a_{n+1}=a_n,\ b_{n+1}=x_n\hspace{20px}f(b_n)f(x_n)\ge0\\ \)

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