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摘要
This paper studies block matrices A = [A(ij)] is an element of C-km (x) (km), where every block A(ij) is an element of C-k (x) (k) for i, j is an element of < m > = {1, 2, . . ., m} and A(ii) is non-Hermitian positive definite for all i is an element of < m >. Such a matrix is called an extended H-matrix if its block comparison matrix is a generalized M-matrix. Matrices of this type are an extension of generalized M-matrices proposed by Elsner and Mehrmann [L. Elsner and V. Mehrmann. Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations. Numer. Math., 59: 541-559, 1991.] and generalized H-matrices by Nabben [R. Nabben. On a class of matrices which arise in the numerical solution of Euler equations. Numer. Math., 63:411-431, 1992.]. This paper also discusses some properties including positive definiteness and invariance under block Gaussian elimination of a subclass of extended H-matrices, especially, convergence of some block iterative methods for linear systems with such a subclass of extended H-matrices. Furthermore, the incomplete LDU-factorization of these matrices is investigated and applied to establish some convergent results on some iterative methods. Finally, this paper generalizes theory on generalized H-matrices and answers the open problem proposed by R. Nabben.
