In this paper, a new preconditioner for a class of $$2\times 2$$ block linear systems is proposed. The proposed new preconditioner is a better approximation to the original coefficient matrix than the previous ones. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are discussed. Finally, two numerical examples are provided to show the effectiveness of the proposed preconditioner.

中文翻译：

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一类 $$2\times 2$$ 块线性系统的新预处理器

在本文中，提出了一种用于$2\times 2$$ 块线性系统类的新预处理器。所提出的新预处理器比以前的预处理器更接近原始系数矩阵。讨论了预处理矩阵的最小多项式的阶数的特征值分布和上界。最后，提供了两个数值例子来说明所提出的预处理器的有效性。