The definitions of θ-ray pattern proposed to establish some new results matrix and θ-ray matrix are firstly on nonsingularity/singularity and convergence of general H-matrices. Then some conditions on the matrix A ...The definitions of θ-ray pattern proposed to establish some new results matrix and θ-ray matrix are firstly 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 E HM and the subset α C （n） such that the Schur complement matrix A/α∈ HI^n-｜α｜ or A/α ∈ Hn-｜α｜^M or A/α ∈ H^n-｜ α｜^S.展开更多
基金Acknowledgements This work was supported in part by the Science Foundation of the Education Department of Shaanxi Province of China （No. 2013JK0593）, the Scientific Research Foundation of Xi＇an Polytechnic University （No. BS1014）, the China Postdoctoral Science Foundation （No. 20110491668）, and the National Natural Science Foundations of China （Grant Nos. 11201362, 11271297, 11101325, 11171270）.
文摘The definitions of θ-ray pattern proposed to establish some new results matrix and θ-ray matrix are firstly 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 E HM and the subset α C （n） such that the Schur complement matrix A/α∈ HI^n-｜α｜ or A/α ∈ Hn-｜α｜^M or A/α ∈ H^n-｜ α｜^S.
