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The optimal parameter of the Hermitian/skew-Hermitian splitting (HSS) iteration method for a real two-by-two linear system is obtained. The result is used to determine the optimal parameters for linear systems associated with certain two-by-two block matrices and to estimate the optimal parameters of the HSS iteration method for linear systems with n-by-n real coefficient matrices. Numerical examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

Suppose A-BXB*, A-BX -X*B*, and A-BX +X*B* are three linear matrix expressions over the field of complex numbers, where A is an Hermitian or skew-Hermitian matrix. In this paper, we consider how to choose an Hermitian or skew-Hermitian matrix X such that A-BXB* have the maximal and minimal possible ranks, and how to choose X such that A - BX ± X*B* attain the minimal possible ranks. Some applications to Hermitian or skew-Hermitian solutions of matrix equations with symmetric patterns are also given. [ABSTRACT FROM AUTHOR]