10/8/2010
1
Bisection Method
Major: All Engineering Majors
Authors: Autar Kaw, Jai Paul
Transforming Numerical Methods Education for STEM
Undergraduates

Bisection Method

3
Basis of Bisection Method
Theorem
x
f(x)
x
u
x
An equation f(x)=0, where f(x) is a real continuous function,
has at least one root between x
l
and x
u
if f(x
l
) f(x
u
) < 0.
Figure 1
At least one root exists between the two points if the function is
real, continuous, and changes sign.

x
f(x)
x
u
x
6
Basis of Bisection Method
Figure 4
If the function
changes sign between two points,
more than one root for the equation
may exist between the two
points.
( )
x
f
( )
0
=
x
f

7
Algorithm for Bisection Method

8
Step 1
Choose x
and x
u
as two guesses for the root such that
f(x
) f(x
u
) < 0, or in other words, f(x) changes sign
between x
and x
u
. This was demonstrated in Figure 1.
x
f(x)
x
u
x
Figure 1