 Site Statistics  |   Contact  |   About Us       Thursday, October 29, 2020  ~ Newton-Raphson ~ Vieta Methods ~ Birge Method     FIXED POINT METHOD
Fixed Point

The idea behind the fixed point method is very simple: to find the solutions of a given nonlinear function f(x) = 0, it is possible to rearrange f(x)= 0 into the form x = g(x), where g(x) denotes a function of x. Then, simply start with an initial guess, x0 and apply the iteration process:

 xn = g(xn - 1)     for n = 1,2,3,...

For example, to find solutions for the following nonlinear equation:

 f(x) = sin x + ex + x2 - 2x = 0

There are several ways to rewrite the above equation into the form x = g(x). For example, it is possible to rearrange the above equation into the following form:

 x = 1/2(sin x + ex + x2)

Or can be rearranged as:

 x = √2x - sin x - ex  Math, Analysis,
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