Further results on H-matrices and their Schur complements
Further results on H-matrices and their Schur complements
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DOI：
10.1016/j.amc.2007.09.001
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发表时间：
2008-05
期刊：
影响因子：
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通讯作者：
L. Cvetković;V. Kostić;Maja Kovacevic;T. Szulc
中科院分区：
文献类型：
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作者：
L. Cvetković;V. Kostić;Maja Kovacevic;T. Szulc
这是众所周知的[D. Carlson、T. Markham、Schur 对角占优矩阵的补集，捷克语。数学。 J. 29 (104) (1979) 246–251, [1]] 严格对角占优矩阵的 Schur 补是严格对角占优的。此外，如果一个矩阵是 H 矩阵，那么它的 Schur 补也是 H 矩阵 [J.刘，黄，H 矩阵和对角占优矩阵的 Schur 补的一些性质，线性代数应用。 389（2004）365-380，[8]]。最近的研究表明，相同类型的陈述适用于 H 矩阵的一些特殊子类，例如，参见 Liu 等人。 [J。刘，Y.黄，F.张，广义双对角占优矩阵的Schur补，线性代数应用。 378（2004）231-244]。本文的目的是表明，通过使用“缩放”方法，可以显着简化这些结果的证明，如Zhang等人。 [F.张等人，The Schur Complement and its applications, Springer, New York, 2005] 并给出了这种类型的另一个不变性结果。
It is well-known [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J. 29 (104) (1979) 246–251, [1]] that the Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant. Also, if a matrix is an H-matrix, then its Schur complement is an H-matrix, too [J. Liu, Y. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365–380, [8]]. Recent research showed that the same type of statement holds for some special subclasses of H-matrices, see, for example, Liu et al. [J. Liu, Y. Huang, F. Zhang, The Schur complements of generalized doubly diagonally dominant matrices, Linear Algebra Appl. 378 (2004) 231–244]. The aim of this paper is to show that the proof of these results can be significantly simplified by using “scaling” approach as in Zhang et al. [F. Zhang et al., The Schur Complement and its Applications, Springer, New York, 2005] and to give another invariance result of this type.