# Bisection method

## Calculates the root of the given equation f(x)=0 using Bisection method.

 Select a and b such that f(a) and f(b) have opposite signs. The convergence to the root is slow, but is assured.This method is suitable for finding the initial values of the Newton and Halley’s methods.
f(x)
a
 , b f(a)f(b)≦0
 maximum repetition n 10 20 50 100 200 500
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Bisection\ method\\[10](1)\ initial\ value\qquad a_0,\ b_0\hspace{20}f(a_0)f(b_0)\le0\\(2)\ x_n={\large\frac{a_n+b_n}{2}}\\\hspace{25}f(x_n)\le\varepsilon\ \Rightarrow\ answer=x_n\\\hspace{25} a_{n+1}=x_n,\ b_{n+1}=b_n\hspace{20}f(a_n)f(x_n)\ge0\\\hspace{25} a_{n+1}=a_n,\ b_{n+1}=x_n\hspace{20}f(b_n)f(x_n)\ge0\\$
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