D-iteration method or how to improve Gauss-Seidel method
For researchers in numerical linear algebra and graph algorithms, this work offers a new perspective on iterative methods, but the results are preliminary and lack concrete performance numbers.
The paper presents a fluid diffusion-based algorithm for matrix inversion, showing it can outperform the Gauss-Seidel method, and discusses theoretical challenges and applications to PageRank.
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.