A note on comparison theorems for splittings and multisplittings of Hermitian positive definite matrices

AbstractWe discuss iterative methods for the solution of the linear system Ax = b, which are based on a single splitting or a multisplitting of A. In order to compare different methods, it is common to compare the spectral 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 matrices. Furthermore, we establish a comparison theorem for multisplittings of a Hermitian positive definite matrix