Bulletin of the
Korean Mathematical Society BKMS

We consider fixed-point iterations constructed by simple \linebreak transforming from a quadratic matrix equation to equivalent fixed-point equations and assume that the iterations are well-defined at some solutions. In that case, we suggest real valued functions. These functions provide radii at the solution, which guarantee the local convergence and the uniqueness of the solutions. Moreover, these radii obtained by simple calculations of some constants. We get the constants by arbitrary matrix norm for coefficient matrices and solution. In numerical experiments, the examples show that the functions give suitable boundaries which guarantee the local convergence and the uniqueness of the solutions for the given equations.

Keywords: quadratic matrix equation (QME), functional iteration, fixed-point iterative method, contraction mapping theorem

MSC numbers: 15A24, 65F10, 65H10