Solving system of equations iteratively

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I have the following system of equations:

$$ \boldsymbol{X}_{n+1} = \boldsymbol{X}_{0} + \boldsymbol{X}_{n} $$

Where $\boldsymbol{X}_{0}$ is my initial calculation and each of the $\boldsymbol{X}$ is a vector.

What methods are there to solve this iteratively?