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Convergence of $ \vec{x_{n+1}} = A^{-1} f(\vec{x_{n}},\vec{y_{n}}), \:\:\: \vec{y_{n+1}} = A^{-1} g(\vec{x_{n}},\vec{y_{n}}) $
I have two systems
$$ A \vec{x} = f(\vec{x}, \vec{y}), \:\:\: A \vec{y} = g(\vec{x}, \vec{y}) $$
Both have the same constant, square, invertible matrix $A$. I implemented an iterative algorithm with ...