TWO INVERSION-FREE ITERATIVE ALGORITHMS FOR COMPUTING THE MAXIMAL POSITIVE DEFINITE SOLUTION OF THE NONLINEAR MATRIX EQUATION

In this paper, we propose two inversion-free iterative algorithms for obtaining the maximal positive definite solution of the nonlinear matrix equations X ± A^TX - α A = Q with the case α 0. We prove that the sequences generated by the proposed iterative schemes are monotonically increasing and bounded above. Some numerical results are also reported in the paper, which confirm the good theoretical properties of our approach