Let $(f^0, g^0) \in \mathbb{R}^{I \times J}$. For all $k \geq 0$, we consider $$g^{k+1} = g_*(f^k) \text{ and } f^{k+1} = f_*(g^{k+1})$$ Show that the sequence $(G(f^k, g^k))_{k \geq 0}$ is increasing.
Let $(f^0, g^0) \in \mathbb{R}^{I \times J}$. For all $k \geq 0$, we consider
$$g^{k+1} = g_*(f^k) \text{ and } f^{k+1} = f_*(g^{k+1})$$
Show that the sequence $(G(f^k, g^k))_{k \geq 0}$ is increasing.