The error correction methods such as multigrid, subspace, deflation, implicit error correction methods are widely used for the acceleration of the convergence of iterative methods. The solution of a series of linear systems with an identical coefficient matrix or similar ones is focused on. We introduce a novel construction method of the mapping operators of the error correction method in this situation. The mapping operator is generated by using the information obtained in the preceding solution process. Numerical tests examine the effectiveness of the proposed method.