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>The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices
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The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices
The result on the Geršgorin disc separation from the origin for strictly diagonally dominant matrices and their Schur complements in (Liu and Zhang in SIAM J. Matrix Anal. Appl. 27(3):665-674, ) is extended to nonstrictly diagonally dominant matrices and their Schur complements, showing that under some conditions the separation of the Schur complement of a nonstrictly diagonally dominant matrix is greater than that of the original grand matrix. As an application, the eigenvalue distribution of the Schur complement is discussed for nonstrictly diagonally dominant matrices to derive some significant conclusions. Finally, some examples are provided to show the effectiveness of theoretical results.
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机译：Geršgorin光盘从严格对角优势矩阵及其Schur补码的原点分离出来的结果（SIAM J. Matrix Anal。Appl。27（3）：665-674，的Liu和Zhang）扩展到非严格对角优势矩阵以及它们的Schur补体，表明在某些条件下，非严格对角优势矩阵的Schur补体的分离要大于原始大矩阵的Schur补体。作为应用，针对非严格对角占优矩阵讨论了Schur补的特征值分布，以得出一些重要结论。最后，通过一些例子说明了理论结果的有效性。
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