The Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices and its applications
The Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices and its applications
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Nekrasov矩阵Schur补上的Nekrasov对角显性度及其应用
DOI：
10.1016/j.amc.2017.09.032
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发表时间：
2018
影响因子：
4
通讯作者：
Tu Gen
中科院分区：
文献类型：
--
作者：
Liu Jianzhou;Zhang Juan;Zhou Lixin;Tu Gen
在本文中，我们估计 Nekrasov 矩阵的 Schur 补上的 Nekrasov 对角优势度。作为一种应用，我们为几个特殊矩阵提供了行列式的新界，在某些情况下改善了相关结果。此外，我们给出了 Nekrasov 矩阵 Schur 补的逆无穷范数界的估计。最后，我们引入了基于 Schur 的超松弛迭代（SSSOR）方法和基于 Schur 的共轭梯度（SCG）方法的新方法来通过降阶来求解线性方程。数值算例说明了推导结果的有效性。
In this paper, we estimate the Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices. As an application, we offer new bounds of the determinant for several special matrices, which improve the related results in certain case. Further, we give an estimation on the infinity norm bounds for the inverse of Schur complement of Nekrasov matrices. Finally, we introduce new methods called Schur-based super relaxation iteration (SSSOR) method and Schur-based conjugate gradient (SCG) method to solve the linear equation by reducing order. The numerical examples illustrate the effectiveness of the derived result.