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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 todoi:10.4236/am.2018.96052 fatcat:btbhf4pi5vh5jkl2igl4kvyfti