Convergence of block iterative methods for linear systems with generalized H-matrices

The paper studies the convergence of some block iterative methods for the solution of linear systems when the coefficient matrices are generalized HH-matrices. A truth is found that the class of conjugate generalized HH-matrices is a subclass of the class of generalized HH-matrices and the convergence results of R. Nabben [R. Nabben, On a class of matrices which arises in the numerical solution of Euler equations, Numer. Math. 63 (1992) 411–431] are then extended to the class of generalized HH-matrices. Furthermore, the convergence of the block AOR iterative method for linear systems with generalized HH-matrices is established and some properties of special block tridiagonal matrices arising in the numerical solution of Euler equations are discussed. Finally, some examples are given to demonstrate the convergence results obtained in this paper.