A New Inversion-Free Iterative Scheme to Compute Maximal and Minimal Solutions of a Nonlinear Matrix Equation

Malik Zaka Ullah
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Malik Zaka Ullah: Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2021, vol. 9, issue 23, 1-7

Abstract: 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.

Keywords: iterative method; inversion-free; nonlinear matrix equations; Hermitian (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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