Some new sufficient conditions for generalized strictly diagonally dominant matrices
نویسندگان
چکیده
Generalized strictly diagonally dominant matrices have wide applications in science and engineering, but it is very difficult to determine whether a given matrix is a generalized strictly diagonally dominant matrix or not in practice. In this paper, we give several practical conditions for generalized strictly diagonally dominant matrices by constructing different positive diagonal matrix and applying some techniques of inequalities, which improve and generalize some existing conclusions. Effectiveness of results is illustrated by some numerical examples.
منابع مشابه
Subdirect sums of doubly diagonally dominant matrices
The problem of when the k-subdirect sum of a doubly diagonally dominant matrix (DDD matrix) is also a DDD matrix is studied. Some sufficient conditions are given. The same situation is analyzed for diagonally dominant matrices and strictly diagonally dominant matrices. Additionally, some conditions are also derived when card(S)>card(S1) which was not studied by Bru, Pedroche and Szyld [Electron...
متن کاملA note on the convergence of the generalized AOR iterative method for linear systems
Recently, some convergent results of the generalized AOR iterative (GAOR) method for solving linear systems with strictly diagonally dominant matrices are presented in [Darvishi, M.T., Hessari, P.: On convergence of the generalized AOR method for linear systems with diagonally dominant cofficient matrices. Appl. Math. Comput. 176, 128-133 (2006)] and [Tian, G.X., Huang, T.Z., Cui, S.Y.: Converg...
متن کاملGeneralizations of Diagonal Dominance in Matrix Theory
A matrix A ∈ C is called generalized diagonally dominant or, more commonly, an H−matrix if there is a positive vector x = (x1, · · · , xn) such that |aii|xi > ∑ j 6=i |aij|xj, i = 1, 2, · · · , n. In this thesis, we first give an efficient iterative algorithm to calculate the vector x for a given H-matrix, and show that this algorithm can be used effectively as a criterion for H-matrices. When ...
متن کاملDoubly Diagonally Dominant Matrices
We consider the class of doubly diagonally dominant matrices (A = [ ajj] E C”, ‘, la,,1 l”jjl > Ck+ i laiklCk+ jlajkl. i #j) and its subclasses. We give necessary and sufficient conditions in terms of the directed graph for an irreducibly doubly diagonally dominant matrix to be a singular matrix or to be an H-matrix. As in the case of diagonal dominance, we show that the Schur complements of do...
متن کاملConditions for separability in generalized Laplacian matrices and nonnegative matrices as density matrices
Recently, Laplacian matrices of graphs are studied as density matrices in quantum mechanics. We continue this study and give conditions for separability of generalized Laplacian matrices of weighted graphs with unit trace. In particular, we show that the Peres-Horodecki positive partial transpose separability condition is necessary and sufficient for separability in C2 ⊗ C. In addition, we pres...
متن کامل