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The traditional matrix decomposition model cannot fully explored the intrinsic relationship between the user and the object in the mean, bias and characteristics. This paper proposed a fitting matrix model to improve the prediction performance by constructing the user and the item matrix to represent the characteristics of the user and the item respectively. The matrix decomposition model had the advantage of accuracy in the field of recommender system, but the gradient descent method, which was the most popular method to train parameters of model, had a slow convergence speed. To resolve the above defects, this paper considered to accelerate the convergence speed using the convergence of quasi Newton method, and named the proposed algorithm as fitting matrix and two orders fusion iterative (FAST) algorithm. The experimental results show that the FAST algorithm is better than the traditional non negative matrix decomposition (NMF), singular value matrix decomposition (SVD), and the regularized singular value matrix decomposition (RSVD). FAST algorithm has a decrease with regard to the mean absolute error (MAE) and the root mean square error (RMSE), and has a significant improvement in the iterative efficiency, which alleviates the problem that the accuracy is difficult to balance with the efficiency of the iteration. [ABSTRACT FROM AUTHOR]