A New Inversion-free Iterative Method for Solving the Nonlinear Matrix Equation and Its Application in Optimal ControlOA
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
GAO Xiangyu;XIE Weiwei;ZHANG Lina
School of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,ChinaSchool of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,ChinaTeaching Affairs Office,Guangxi Normal University,Guilin 541004,China
数理科学
Nonlinear matrix equationMaximal positive definite solutionInversion-free iterative methodOptimal control
《应用数学》 2026 (1)
P.143-150,8
Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government''s Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
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