intersects the x-axis in two places.
Activities
Numerical methods of solving equations - one point iterative methods
.
| There are two real solutions as
the graph of
intersects the x-axis in two places. |
|
.
Any such rearrangement can be used
as an iterative process 
to produce a sequence of numbers.
Different starting numbers can be tried to see whether the sequence converges to a limit. Any limit that exists is a solution of the equation.
Rearrangement 1
Suppose the starting number is 4.
The screen shots show that the sequence converges to the limit 2.0697 (accurate to 4 decimal places). This is one of the two solutions of the equation
.
Try other starting values. Can you find the other solution (approximately -1)?
Having difficulties? Try different rearrangements. (See 2 or 3.)
How can we tell whether an iterative
process
will converge to a particular solution?
It depends on:
.
