Journal
MATHEMATICS
Volume 9, Issue 23, Pages -Publisher
MDPI
DOI: 10.3390/math9232994
Keywords
iterative method; inversion-free; nonlinear matrix equations; Hermitian
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Funding
- Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia [FP-163-43]
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This article investigates a new solver in the form of an iterative method for solving an important nonlinear matrix equation, discussing the minimal and maximal solutions as Hermitian positive definite matrices. The convergence of the scheme is confirmed, supported by several numerical tests.
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. 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.
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