Abstract
The goal of this article is to investigate a new solver in the form of an iterative method to solve X+A∗X−1A=I as an important nonlinear matrix equation (NME), where A,X,I are appropriate matrices. The minimal and maximal solutions of this NME are discussed as Hermitian positive definite (HPD) matrices. The convergence of the scheme is given. Several numerical tests are also provided to support the theoretical discussions.
Highlights
IntroductionWhere YS is the minimal solution of the dual nonlinear matrix equation (NME) as follows: Publisher’s Note: MDPI stays neutral
The goal of this article is to investigate a new solver in the form of an iterative method to solve X + A∗ X −1 A = I as an important nonlinear matrix equation (NME), where A, X, I are appropriate matrices
Where YS is the minimal solution of the dual NME as follows: Publisher’s Note: MDPI stays neutral
Summary
Where YS is the minimal solution of the dual NME as follows: Publisher’s Note: MDPI stays neutral. In several disciplines such as control theory, stochastic filtering, queuing theory, etc., this type of nonlinear equation typically appears, see [6,7,8] for further discussions. It is always a daunting task to find a positive definite solution (PDS) to an NME [9,10] This is because most of the existing methods are computationally expensive due to presence of the inverse part in each loop, see the discussions given in [11,12]
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