Fixed point iteration method

The fixed point iteration method uses the concept of a fixed point in a repeated manner to compute the solution of the given equation. A fixed point is a point in the domain of a function g such that g(x) = x. In the fixed point iteration method, the given function is algebraically converted in the form of g(x) = x.

1. What is a fixed point equation?
2. What are the advantages of fixed point method?
3. Does fixed-point iteration always converge?

What is a fixed point equation?

Fixed point : A point, say, s is called a fixed point if it satisfies the equation x = g(x). Fixed point Iteration : The transcendental equation f(x) = 0 can be converted algebraically into the form x = g(x) and then using the iterative scheme with the recursive relation.

What are the advantages of fixed point method?

Memory Usage and Speed — In general fixed-point calculations require less memory and less processor time to perform. Cost — Fixed-point hardware is more cost effective where price/cost is an important consideration.

Does fixed-point iteration always converge?

As discussed above, fixed-point iteration will converge for any initial guess, so we choose x0 = 0.5.