FIXED POINT

Is an iterative method that allows solving systems of equations that are not necessarily linear. In particular, it can be used to determine roots of a function of the form f(x), as long as the convergence criteria are met.

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The fixed-point iteration method, also called the successive approximation method, requires rewriting the equation f(x)=0 in the form x=g(x)

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Let's call x* the root of f. Suppose that the function g exists and is known such that:

f(x)= x-g(x) ∀ of the domain.

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so:

f(x*)=0 <->x*-g(x*)=0 <-> x*=g(x) 

 

we have x as a fixed point of g. 

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