Thompson metric method for solving a class of nonlinear matrix equation
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摘要
Based on the elegant properties of the Thompson metric, we prove that the general nonlinear matrix equation Xq-A∗F(X)A=Q(q>1) always has a unique positive definite solution. An iterative method is proposed to compute the unique positive definite solution. We show that the iterative method is more effective as q increases. A perturbation bound for the unique positive definite solution is derived in the end.
论文关键词:Nonlinear matrix equation,Positive definite solution,Iterative method,Perturbation bound,Thompson metric
论文评审过程:Available online 24 December 2009.
论文官网地址:https://doi.org/10.1016/j.amc.2009.12.022