An algorithm for computing positive definite solutions of the nonlinear matrix equation X + A*X⁻¹A = I

Abstract

In this paper, an algorithm for obtaining the Hermitian positive definite solutions of the nonlinear matrix equation X + A*X ⁻¹ A = I is considered and discussed. The convergence of the algorithm is proved. Numerical experiments to illustrate the behavior of the algorithm are executed.

Keywords:

• Nonlinear matrix equation
• Iteration methods
• Convergence of sequences
• Positive definite matrix