Abstract
Motivated by the classical Newton–Schulz method for finding the inverse of a nonsingular matrix, we develop a new inversion-free method for obtaining the minimal Hermitian positive definite solution of the matrix rational equation X + A ∗ X - 1 A = I , where I is the identity matrix and A is a given nonsingular matrix. We present convergence results and discuss stability properties when the method starts from the available matrix AA ∗ . We also present numerical results to compare our proposal with some previously developed inversion-free techniques for solving the same rational matrix equation.
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