Iteration Method Let the given equation be f(x) = 0 and the value of x to be determined. By using the Iteration method you can find the roots of the equation. To find the root of the equation first we have to write equation like below
x = pi(x)
Let x=x_{0} be an initial approximation of the required root α then the first approximation x_{1} is given by x_{1} = pi(x0).

Similarly for second, thrid and so on. approximation
x_{2} = pi(x_{1})
x_{3} = pi(x_{2})
x_{4} = pi(x_{3})
x_{n} = pi(x_{n-1})

Iteration Method Example: Find the real root of the equation x^{3} + x ^{2} = 1 by iteration method.
Solution:
We can rewrite the above equation by
x^{3} + x ^{2} - 1 = 0;
Let f(x) = x^{3} + x ^{2} - 1
f(0) = -1 (positive)
f(1) = 1 (negative)
Hence the root value lie between 0 to 1

Since the difference between x_{6} and x_{7} are very small, so the root is 0.75488.

Iteration method Practice problem: 1. Solve by iteration method 2x - logx - 7 = 0
2. Find the root of the equation x log x = 1.2 by iteration method
3. Compute the real root of 3x - cosx - 1 = 0 by iteration method
4. Find the root of the equation sin x = 1 + x3 between ( -2,-1) to 3 decimal places by Iteration method