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<p>Diagonal-Schur complement is a hot topic in Matrix theory. The class of SDD<sub>1</sub> matrices is an important subclass of nonsingular H-matrices. In this paper, we prove that the diagonal-Schur complements of SDD<sub>1</sub> matrices are also SDD<sub>1</sub> matrices with respect to any principal sub-matrix. We introduce the concept of the corresponding diagonally dominant degree. Then the SDD<sub>1</sub> diagonally dominant degrees of diagonal-Schur complements are estimated. The numerical results are reported.</p>

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Diagonal-schur complements of SDD1 matrices

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Shiyun Wang,
  • Yun Li,
  • Zhen-Hua Lyu

摘要

Diagonal-Schur complement is a hot topic in Matrix theory. The class of SDD1 matrices is an important subclass of nonsingular H-matrices. In this paper, we prove that the diagonal-Schur complements of SDD1 matrices are also SDD1 matrices with respect to any principal sub-matrix. We introduce the concept of the corresponding diagonally dominant degree. Then the SDD1 diagonally dominant degrees of diagonal-Schur complements are estimated. The numerical results are reported.