A note on the parallel GSAOR method for block diagonally dominant matrices

A 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...

Ela the Eigenvalue Distribution of Block Diagonally Dominant Matrices and Block H−matrices

The paper studies the eigenvalue distribution of some special matrices, including block diagonally dominant matrices and block H−matrices. A well-known theorem of Taussky on the eigenvalue distribution is extended to such matrices. Conditions on a block matrix are also given so that it has certain numbers of eigenvalues with positive and negative real parts.

A Note on Estimates of Diagonal Elements of the Inverse of Diagonally Dominant Tridiagonal Matrices

In this note we show how to improve some recent upper and lower bounds for the elements of the inverse of diagonally dominant tridiagonal matrices. In particular, a technique described by [R. Peluso, and T. Politi, Some improvements on two-sided bounds on the inverse of diagonally dominant tridiagonal matrices, Lin. Alg. Appl. Vol. 330 (2001) 1-14], is used to obtain better bounds for the diago...

A note on nonnegative diagonally dominant matrices

Generalizations 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 ...