General <i>H</i>-matrices and their Schur complements

doi:10.1007/s11464-014-0395-1

Front. Math. China

2014, Vol. 9

Issue (5) : 1141-1168 https://doi.org/10.1007/s11464-014-0395-1

RESEARCH ARTICLE

General H-matrices and their Schur complements

Cheng-yi ZHANG^1,², Fengmin XU¹(

), Zongben XU¹, Jicheng LI¹

¹. Institute of Information and system Science and School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
². School of Science, Xi’an Polytechnic University, Xi’an 710048, China

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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

Corresponding Author(s): Fengmin XU

Issue Date: 26 August 2014

Cite this article:

Cheng-yi ZHANG,Fengmin XU,Zongben XU, et al. General H-matrices and their Schur complements[J]. Front. Math. China, 2014, 9(5): 1141-1168.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0395-1
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I5/1141

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