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2014•Journal of Science of Teachers' College and UniversityRequires access

Inverse-free iterative algorithm for nonlinear matrix equation X~α+A~*X~(-1)A=Q

Fan Guang-hu

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Abstract

Nonlinear matrix equation Xα+A*X-1A=Q,where A,Q are n×n complex matrices with Q Hermitian positive definite,has widely applied background.An inverse-free iterative algorithm for obtaining the maximal Hermitian positive definite solution of the above nonlinear matrix equation was proposed when α≥1.And numerical example was given to show the efficiency of the proposed iterative method.Key words:nonlinear matrix equation;inverse-free iterative method;maximal solution

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What this paper is about

Nonlinear matrix equation Xα+A*X-1A=Q,where A,Q are n×n complex matrices with Q Hermitian positive definite,has widely applied background.An inverse-free iterative algorithm for obtaining the maximal Hermitian positive definite solution of the above nonlinear matrix equation was proposed when α≥1.And numerical example was given to show the efficiency of the proposed iterative method.Key words:nonlinear matrix equation;inverse-free iterative method;maximal solution

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Available abstract

Nonlinear matrix equation Xα+A*X-1A=Q,where A,Q are n×n complex matrices with Q Hermitian positive definite,has widely applied background.An inverse-free iterative algorithm for obtaining the maximal Hermitian positive definite solution of the above nonlinear matrix equation was proposed when α≥1.And numerical example was given to show the efficiency of the proposed iterative method.Key words:nonlinear matrix equation;inverse-free iterative method;maximal solution

Key concepts: Mathematics, Iterative method, Hermitian matrix, Inverse, Positive-definite matrix, Matrix (chemical analysis), Nonlinear system, Applied mathematics

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