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Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X+A*X-1A=Q

Author

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  • Engwerda, J.C.

    (Tilburg University, Faculty of Economics)

  • Ran, A.C.M.
  • Rijkeboer, A.L.

Abstract

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Suggested Citation

  • 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," Research Memorandum FEW 534, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiurem:cbc6bc1e-3bbf-49a4-8222-d7f68b516268
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    Cited by:

    1. Chang-Zhou Li & Chao Yuan & An-Gang Cui, 2023. "Newton’s Iteration Method for Solving the Nonlinear Matrix Equation X + ∑ i = 1 m A i * X − 1 A i = Q," Mathematics, MDPI, vol. 11(7), pages 1-11, March.
    2. 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.
    3. Nashine, Hemant Kumar & Bose, Snehasish, 2019. "Solution of a class of cross-coupled nonlinear matrix equations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    4. Sbrana, Giacomo & Poloni, Federico, 2013. "A closed-form estimator for the multivariate GARCH(1,1) model," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 152-162.
    5. Malik Zaka Ullah, 2021. "A New Inversion-Free Iterative Scheme to Compute Maximal and Minimal Solutions of a Nonlinear Matrix Equation," Mathematics, MDPI, vol. 9(23), pages 1-7, November.

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    Keywords

    Matrices; numerieke wiskunde;

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