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Hasanov, V.I. (2005) Positive Definite Solutions of the Matrix Equations . Linear Algebra and Its Applications, 404, 166-182.
https://doi.org/10.1016/j.laa.2005.02.024

has been cited by the following article:

• TITLE: Iterative Methods for Solving the Nonlinear Matrix Equation X-A*XpA-B*X-qB=I (0p,q

  AUTHORS: Dongjie Gao

  KEYWORDS: Nonlinear Matrix Equation, Positive Definite Solution, Iterative Method, Normal Cone

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.7 No.3, September 27, 2017

  ABSTRACT: Consider the nonlinear matrix equation X-A*XpA-B*X-qB=I (0p,q1). By using the fixed point theorem for mixed monotone operator in a normal cone, we prove that the equation with 0p,q1 always has the unique positive definite solution. Two different iterative methods are given, including the basic fixed point iterative method and the multi-step stationary iterative method. Numerical examples show that the iterative methods are feasible and effective.