General H-matrices and their Schur complements

Cheng-yi ZHANG, Fengmin XU, Zongben XU, Jicheng LI

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PDF(234 KB)
Front. Math. China ›› 2014, Vol. 9 ›› Issue (5) : 1141-1168. DOI: 10.1007/s11464-014-0395-1
RESEARCH ARTICLE

General H-matrices and their Schur complements

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Abstract

The definitions of θ-ray pattern matrix and θ-ray matrix are firstly proposed to establish some new results on nonsingularity/singularity and convergence of general H-matrices. Then some conditions on the matrix A C n × n and nonempty α n = { 1 , 2 , , n } are proposed such that A is an invertible H-matrix if A(α) and A/α are both invertible H-matrices. Furthermore, the important results on Schur complement for general H-matrices are presented to give the different necessary and sufficient conditions for the matrix A H n M and the subset α n such that the Schur complement matrix A / α H n | α | I o r A / α H n | a | M o r A / α H n | α | S.

Keywords

Schur complement / convergence / general H-matrices

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Cheng-yi ZHANG, Fengmin XU, Zongben XU, Jicheng LI. General H-matrices and their Schur complements. Front. Math. China, 2014, 9(5): 1141‒1168 https://doi.org/10.1007/s11464-014-0395-1

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