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As the power grid networks become larger and smarter, their operation and control become even more challenging due to the size of the underlying mathematical problems that need to be solved in real-time. In this paper, we report our experience on utilizing the main stream computation architecture to improve performance of solving a system of linear equations, the key part of most power system applications, using iterative methods. Since Conjugate Gradient (CG) algorithms have been applied to power system applications in the literature with a suggested benefit from parallelization, they are selected and evaluated against the mainstream computation architectures (i.e., multi-core CPU and many-core GPU) in the context of both power system state estimation and power flow applications. The evaluation results show that solving a system of linear equations using iterative methods is highly memory bonded and multi-core CPU and GPU computation architecture have different impacts on the performance of such an iterative solver: unlike multicore CPU, GPU can greatly improve the performance of CG-based iterative solver when matrices are well conditioned as typically encountered in the DC power flow formulation.