The fixed point iteration method is an unsystematic method of solving a frequently complex equation by iteration.
The advantage of the method is its simplicity. We do not need to calculate the first or higher derivative. Thus it would work even with tabular functions. Another advantage, which is common to most iterative methods, is that it is self correcting. If a minor calculation error is made, it will still converge to the correct answer at the end.
The disadvantage of the method is that it is unsystematic. We do not know if it will converge to a solution, and if it does, which solution. The way to obtain different solutions is to rearrange the iterative formula. Sometimes by rearranging, a different solution can be obtained.
For more information, see:
http://en.wikipedia.org/wiki/Fixed_point_iteration
Post if you need clarifications.
For the fixed point iteration method; re-arranging method, how can I describe ho the iterative formula works?
3 answers
How can I say that the re-arranging method is less efficient with using the iterative formula than the Newton - Raphson Method?
The fixed point iteration method is less efficient (in general) because the efficiency is undefined and problem dependent.
The Newton-Raphson method depends on the derivative of the function. With very few exceptions, such as near asymptotes, convergence is second-order. In most cases, the number of digits of accuracy doubles with each iteration.
With fixed-point iteration, convergence is not even guaranteed, and not rapid, unless it "happens" to coincide with the Newton-Raphson formula.
The Newton-Raphson method depends on the derivative of the function. With very few exceptions, such as near asymptotes, convergence is second-order. In most cases, the number of digits of accuracy doubles with each iteration.
With fixed-point iteration, convergence is not even guaranteed, and not rapid, unless it "happens" to coincide with the Newton-Raphson formula.