In this paper, we first introduce the necessary and sufficient conditions for the existence of
the solution of discrete algebraic Riccati equation. Then we propose the Newton method …

The non-symmetric algebraic Riccati equation (NARE) occurs in several areas of applied
mathematics and engineering such as spectral factorizations of rational matrix functions …

The quadratic nonlinear matrix equation Q (Y)= MY 2+ N Y+ P, occurs in many applications
such as the Quasi-Birth-Death processes, pseudo-spectra for quadratic eigenvalue …

The quadratic matrix equation (QME) Q (X)= AX 2+ BX+ C= 0, Q (X)= AX^ 2+ BX+ C= 0,
occurs in the branches such as the quadratic eigenvalue problems and quasi‐birth‐death …

Purpose In this paper, the authors study the nonlinear matrix equation X p= Q±A (X-1+ B)-1
AT, that occurs in many applications such as in filtering, network systems, optimal control …

Nonlinear matrix equations have important applications in optimal control problems. This
study introduces parametric iterative methods aimed at determining solutions for the …

In this paper, we initially introduce several theoretical results regarding the existence of
solutions for the nonlinear tensor equation X+ AT∗ NX-1∗ NA= I. Then, we present iterative …

In this paper, we investigate the iterative methods for the solution of different types of
nonlinear matrix equations. More specifically, we consider iterative methods for the minimal …