On Schur complement of block diagonally dominant matrices

详细信息    查看全文

• 作者：Cheng-yi Zhang ; Yao-tang Li and Feng Chen
• 关键词：Schur complements ; I-(II-)block diagonally dominant matrices ; I-(II-)generalized block diagonally dominant matrices
• 刊名：Linear Algebra and its Applications
• 出版年：2006
• 出版时间：15 April 2006
• 年：2006
• 卷：414
• 期：2-3
• 页码：533-546
• 全文大小：164 K

文摘

It is well-known that the Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J. 29 (104) (1979) 246–251]; the same is true of generalized strictly diagonally dominant matrices [Jianzhou Liu, Yungqing Huang, Some properties on Schur complements of H-matrix and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365–380]. In this paper, this result is extended to the block (strictly) diagonally dominant matrices and the generalized block (strictly) diagonally dominant matrices, that is, it is shown that the Schur complement of a block (strictly) diagonally dominant matrix is a block (strictly) diagonally dominant matrix and so is the Schur complement of a generalized block (strictly) diagonally dominant matrix.