We study residual-based algorithms for computing stationary distributions of large Markov chains. For reversible chains, we show that RLGL can be viewed as coordinate gradient descent on the Dirichlet energy associated with the normalized Laplacian. This viewpoint motivates Gauss--Southwell--Dirichlet (GSD), a modification of the max-residual heuristic that rescales residuals by the square root of the stationary distribution. Experiments show that GSD can substantially improve convergence."