In this paper, we construct a circulant-matrix-based new accelerated GSOR (CNAGSOR) iteration method for a class of large and sparse block two-by-two linear systems of generalized saddle-point structure. Theoretical results about the convergence properties and eigenvalues distribution of the preconditioning matrix are studied in detail. Implementations in the image restoration problem and in the PDE-constraint optimization problem are made to verify the feasibility and the efficiency of the new methods.

中文翻译：

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基于循环矩阵的新加速GSOR预处理方法，用于解决两两线性系统中的图像复原问题

在本文中，我们为一类大型且稀疏的块二乘二线性广义鞍点结构线性系统构造了一种基于循环矩阵的新加速GSOR（CNAGSOR）迭代方法。详细研究了预处理矩阵的收敛性和特征值分布的理论结果。通过对图像恢复问题和PDE约束优化问题的实现，验证了新方法的可行性和有效性。