In this paper, several conditions are presented to keep the Schur complement via a non-leading principle submatrix of some special matrices including Nekrasov matrices being a Nekrasov matrix, which is useful in the Schur-based method for solving large linear equations. And we give some infinity norm bounds for the inverse of Nekrasov matrices and its Schur complement to help measure whether the classical iterative methods are convergent or not. At last, in the applications of solving large linear equations by Schur-based method, some numerical experiments are presented to show the efficiency and superiority of our results.

中文翻译：

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Nekrasove矩阵的Schur补的闭合性质及其在基于Schur的方法求解大型线性系统中的应用

在本文中，提出了一些条件，以通过某些特殊矩阵的非超前原理子矩阵（包括作为Nekrasov矩阵的Nekrasov矩阵）来保持Schur补码，这对于基于Schur的方法求解大型线性方程组很有用。并且我们给出了Nekrasov矩阵及其Schur补的逆的无穷范数界，以帮助衡量经典迭代方法是否收敛。最后，在基于Schur方法求解大型线性方程组的应用中，通过一些数值实验证明了我们的结果的有效性和优越性。