On positive definite solutions of the nonlinear matrix equations X±A*XqA=Q

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摘要

In this paper, we investigate the nonlinear matrix equations X+A*XqA=Q(01). Necessary and sufficient conditions for the (unique) existence of Hermitian positive definite solutions of these equations are derived. Effective iterative algorithms are also provided to obtain the unique solution of X+A*XqA=Q(01). Numerical examples are included to illustrate the efficiency of the presented iteration algorithms.

论文关键词：Nonlinear matrix equations,Positive definite solution,Iterative methods

论文评审过程：Received 4 July 2015, Revised 18 August 2015, Accepted 3 September 2015, Available online 8 October 2015, Version of Record 8 October 2015.

论文官网地址：https://doi.org/10.1016/j.amc.2015.09.002