中文摘要：

本文将鞍点问题转化为一个具有对称正定系数矩阵的等价模型。在同等条件下，将求解鞍点问题的SOR-like方法与等价模型的SOR方法进行了对比，发现等价模型效果更好。此外，我们还提出了一种新的修正Chebyshev加速迭代方法，它的参数是由优化模型而不是Chebyshev多项式产生，并讨论了修正的Chebyshev加速迭代方法的收敛性。最后，通过数值例子比较各种算法的收敛速度和迭代次数，验证了修正的Chebyshev加速迭代方法的收敛性优势。

英文摘要：

In this paper, we equivalently transform the saddle point problem into a new model whose coefficient matrix is a symmetric positive definite matrix. Under similar settings, we compare the proposed SOR method for the equivalent model with the traditional SOR-like method, which are used to solve the saddle point problem, and find that the equivalent model has a better performance. In addition, we propose a modified Chebyshev accelerative iterative method, whose parameter is obtained from an optimization model while not the conventional Chebyshev polynomial. The convergence of the modified Chebyshev accelerative iterative method is also studied. Finally, a numerical example is given to compare the convergence rate and the iteration number of all kinds of algorithms. The results have showed that the modified Chebyshev accelerative iterative method has a better convergence rate than other accelerative iterative methods.