Bisection Method

Also known as method:
• Binary Court.
• Partition.
• Bolzano.

It is a type of incremental search is based on dividing the always in the middle interval and the change of sign on
interval. 

Example:

The equation

t3  + 4 t2  - 1 = 0

has a positive root r in [0,1]. f(0)<0 and f(1)>0.

Since f(0.5) = 0.125 the root is in [0, 0.5].

Since f(0.25) = -0.73 the root is in [0.25, 0.5].

Since f(0.375) = -0.38 the root is in [0.375, 0.5].

Since f(0.4375) = -0.15 the root is in [0.4375, 0.5].

Since f(0.46875) = -0.018 the root is in [0.46875, 0.5].

Since f(0.484375) = 0.05 the root is in [0.46875, 0.484375].

... and so we approach the root 0.472834 It is superfluous to say that it is easy to computerize this method. Then we have the root in less than a second. 

Advantages

1. • You are guaranteed the convergence of the root lock.
2.  Easy implementation.
3. • management has a very clear error.

 
Disadvantages

 

1. • The convergence can be long.
2. No account of the extreme values (dimensions) as possible roots.