# Multivariate fixed point iteration: the wrt variable on both sides of update equation and not are different?

I try to understand more about the update in multivariate fixed point iteration. I saw the examples where the updates have the same variable (the wrt. variable of partial differentiation) on both sides of update equation

$$H_{kj} = \frac{H_{kj}}{\sum_{i}\sum_{k}W_{ik}H_{kj}}$$ $$W_{ik} = \frac{W_{ik}}{\sum_{j}\sum_{k}W_{ik}H_{kj}}$$

I think I also saw the update that the wrt variable is on the LHS. Are there any differences between these two ways? And is it possible that the set of updates for each variable can be mixed: some variables are on the both side of update equation and some are not like this below?

$$H_{lkj} = \sum_{i}\phi_{lki}V_{ij}/\sigma_{l}$$ $$\phi_{lki} = \sum_{j}H_{lkj}V_{ij}/\sigma_{l}$$ $$\sigma_{l} = \sigma_{l}(\sum_{ij}V_{ij}+)\sum_{ijk}\phi_{lki}V_{ij}$$