The Hermitian positive definite solutions of matrix equation X+A~*X~qA=I(q>0)
Yang Shu-lin · Journal of Anhui University · 2009
Considered the nonlinear matrix equation X+A*XqA=I,where A was the n×n complex matrix,I was the n×n identity matrix,A* expressed the matrix A conjugate transpose.With 0q1 and q1,sufficient conditions for the existence of position definite solutions of the equation were given and the basic fixed point iterations for the equation were discussed.The results were illustrated by numerical examples.