Not enough memory for GMRES

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After realizing that Gauss-Seidel is extremely slow for my simulation, i wanted to try GMRES and luckily found the C++ code here without diving into the theory. The size of the matrix in my case is nxn where n=50,000. However, I even cannot initialize the matrix to zero because the computer freezes while initializing it. Is there a memory friendly version of GMRES?