Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations

Summary We discuss block matrices of the formA=[A_ij], whereA_ij is ak×k symmetric matrix,A_ij is positive definite andA_ij is negative semidefinite. These matrices are natural block-generalizations of Z-matrices and M-matrices. Matrices of this type arise in the numerical solution of Euler equations in fluid flow computations. We discuss properties of these matrices, in particular we prove convergence of block iterative methods for linear systems with such system matrices.