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

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  • Li, Lei
  • Wang, Qing-Wen
  • Shen, Shu-Qian

Abstract

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.

Suggested Citation

  • Li, Lei & Wang, Qing-Wen & Shen, Shu-Qian, 2015. "On positive definite solutions of the nonlinear matrix equations X±A*XqA=Q," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 556-566.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:556-566
    DOI: 10.1016/j.amc.2015.09.002
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    References listed on IDEAS

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    1. Engwerda, J.C., 1993. "On the existence of a positive definite solution of the matrix equation X = ATX-1A = I," Other publications TiSEM 9d762863-0dfe-4aeb-8a13-5, Tilburg University, School of Economics and Management.
    2. Engwerda, J.C. & Ran, A.C.M. & Rijkeboer, A.L., 1992. "Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X+A*X-1A=Q," Other publications TiSEM cbc6bc1e-3bbf-49a4-8222-d, Tilburg University, School of Economics and Management.
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