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A regular splitting and potential reduction method is presented for solving a quadratic programming problem with box constraints (QPB) in this paper. A general algorithm is designed to solve the QPB problem and generate a sequence of iterative points. We show that the number of iterations to generate an e-minimum solution or an e-KKT solution by the algorithm is bounded by O O(n2/∈log1/∈+nlong(1+√2n) and the total running time is bounded by O(n2(n + logn +log1/∈ )(n/∈log1/∈ + logn) ) arithmetic operations.