An algorithm to solve matrix equations PH^{T} = G and P = φ P φ T + γγ T

An iterative algorithm is presented for the numerical solution of matrix equations PH^{T} = G and P = \PhiP\Phi^{T} + \Gamma\Gamma^{T} , where P \geq 0 and G, H , and \Phi are given. These equations arise in various identification, network synthesis, and stability analysis problems.