We present an iterative scheme for solving Poisson’s equation in 2D. Using finite differences, we discretize the equation into a Sylvester system, AU +UB = F, involving tridiagonal matrices A and B. The iterations occur on this Sylvester system directly after introducing a deflation-type parameter that enables optimized convergence. Analytical bounds are obtained on the spectral radii of the iteration matrices. Our method is comparable to Successive Over-Relaxation (SOR) and amenable to compact programming via vector/array operations. It can also be implemented within a multigrid framework with considerable improvement in performance as shown herein.