  The aim of this paper is to present the recently proposed fluid diffusion
based algorithm in the general context of the matrix inversion problem
associated to the Gauss-Seidel method. We explain the simple intuitions that
are behind this diffusion method and how it can outperform existing methods.
Then we present some theoretical problems that are associated to this
representation as open research problems. We also illustrate some connected
problems such as the graph transformation and the PageRank problem.
