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

Authors:
Cheng-yi Zhang;Chengxian Xu;Shuanghua Luo
Affiliations:
Department of Mathematics of School of Science, Xi'an Jiaotong University, Xi'an, 710049, PR China;Department of Mathematics of School of Science, Xi'an Jiaotong University, Xi'an, 710049, PR China and SKLMSE Lab., Xi'an Jiaotong University, Xi'an, 710049, PR China;School of Science, Lanzhou University of Technology, Lanzhou, 730050, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

The paper studies the convergence of some block iterative methods for the solution of linear systems when the coefficient matrices are generalized H-matrices. A truth is found that the class of conjugate generalized H-matrices is a subclass of the class of generalized H-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 H-matrices. Furthermore, the convergence of the block AOR iterative method for linear systems with generalized H-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.