1 IntroductionH-matrices have important role in numerical analysis and matrix theory,etc.In thispaper,several practical criteria for H-matrices are obtained,to which the matrix is notnecessary be a diagonally dominant...1 IntroductionH-matrices have important role in numerical analysis and matrix theory,etc.In thispaper,several practical criteria for H-matrices are obtained,to which the matrix is notnecessary be a diagonally dominant matrix,and the numbers of rows which are not diago-nal dominant can be n-1.We introduce the concept of α-diagonally dominant matrix,andby using the concept to investigate H-matrices.展开更多
Suppose that D is a division ring in which there is defined an anti-automorphism α→(?)is involutorial,R is a left vector space over D.Using the given anti-automorphism α→(?),it is easy to turn R into a right vecto...Suppose that D is a division ring in which there is defined an anti-automorphism α→(?)is involutorial,R is a left vector space over D.Using the given anti-automorphism α→(?),it is easy to turn R into a right vector space over D by seting x(?)=ax.Bilinear form g(x,y)connecting the left vector space R and the right vector space R is a Hermitian scalar.展开更多
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
Practical sufficient conditions for the convergence of the AOR method and a practical sufficient condition for H-matrices are studied. The obtained convergence conditions suited to matrices, which need not to be diago...Practical sufficient conditions for the convergence of the AOR method and a practical sufficient condition for H-matrices are studied. The obtained convergence conditions suited to matrices, which need not to be diagonally dominant.展开更多
The class of generalized α-matrices is presented by Cvetkovi?, L. (2006), and proved to be a subclass of H-matrices. In this paper, we present a new class of matrices-generalized irreducible α-matrices, and prove th...The class of generalized α-matrices is presented by Cvetkovi?, L. (2006), and proved to be a subclass of H-matrices. In this paper, we present a new class of matrices-generalized irreducible α-matrices, and prove that a generalized irreducible α-matrix is an H-matrix. Furthermore, using the generalized arithmetic-geometric mean inequality, we obtain two new classes of H-matrices. As applications of the obtained results, three regions including all the eigenvalues of a matrix are given.展开更多
基金Work supported by Sichuan Youth Sci.Tech.Foundation,P.R.China
文摘1 IntroductionH-matrices have important role in numerical analysis and matrix theory,etc.In thispaper,several practical criteria for H-matrices are obtained,to which the matrix is notnecessary be a diagonally dominant matrix,and the numbers of rows which are not diago-nal dominant can be n-1.We introduce the concept of α-diagonally dominant matrix,andby using the concept to investigate H-matrices.
文摘Suppose that D is a division ring in which there is defined an anti-automorphism α→(?)is involutorial,R is a left vector space over D.Using the given anti-automorphism α→(?),it is easy to turn R into a right vector space over D by seting x(?)=ax.Bilinear form g(x,y)connecting the left vector space R and the right vector space R is a Hermitian scalar.
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.
文摘Practical sufficient conditions for the convergence of the AOR method and a practical sufficient condition for H-matrices are studied. The obtained convergence conditions suited to matrices, which need not to be diagonally dominant.
文摘The class of generalized α-matrices is presented by Cvetkovi?, L. (2006), and proved to be a subclass of H-matrices. In this paper, we present a new class of matrices-generalized irreducible α-matrices, and prove that a generalized irreducible α-matrix is an H-matrix. Furthermore, using the generalized arithmetic-geometric mean inequality, we obtain two new classes of H-matrices. As applications of the obtained results, three regions including all the eigenvalues of a matrix are given.
