Abstract: An inversion-free iterative algorithm is presented for
solving nonlinear matrix equation with a stepsize parameter t. The
existence of the maximal solution is discussed in detail, and the
method for finding it is proposed. Finally, two numerical examples
are reported that show the efficiency of the method.
Abstract: In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δi are discussed. An algorithm that avoids matrix inversion with the case -1