A NOTE ON COMPARISON-THEOREMS FOR SPLITTINGS AND MULTISPLITTINGS OF HERMITIAN POSITIVE-DEFINITE MATRICES

We discuss iterative methods for the solution of the linear system Ax = b, which are based on a single splitting or a multisplitting of A. I n order to compare different methods, it is common to compare the spec tral radius of the iterative matrix. For M-matrices A and weak regular splittings there exist well-known comparison theorems. Here, we give a comparison theorem for splittings of Hermitian positive definite mat rices. Furthermore, we establish a comparison theorem for multisplitti ngs of a Hermitian positive definite matrix.