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Iterative Algorithms for the Linear Matrix Equation X + A*XA = I and Some Properties

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Abstract

Two effective iterative methods are constructed to solve the linear matrix equation of the form X + A*XA = I. Some properties of a positive definite solution of the linear matrix equation and the iterates generated by first Algorithm are discussed. Necessary and sufficient conditions for existence of a positive definite solution are derived for \( \| {\rm A} \| < 1 \) and \( \| A \| > 1 \). Necessary and sufficient conditions for existence of a positive definite solution are derived for \( \| {\rm A} \| < 1 \) and \( \| A \| > 1 \). Several numerical examples are given to show the efficiency of the presented iterative methods.

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Author information

Authors and Affiliations

  1. Princess Nourah Bint Abdulrahman University, Riyad, 11643, KSA

    Sana’a A. Zarea

  2. Benha University, Benha, 13518, Egypt

    Salah M. El-Sayed

  3. Hail University, Hail, 1826, KSA

    Amal A. S. Al-Marshdy

Authors
  1. Sana’a A. Zarea
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  2. Salah M. El-Sayed
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  3. Amal A. S. Al-Marshdy
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Correspondence to Sana’a A. Zarea .

Editor information

Editors and Affiliations

  1. Multimedia Engineering College of Engioneering, Mokpo National University, Chonnam, Korea, Republic of (South Korea)

    Gi-Chul Yang

  2. Unit 1, 1/F, Hung To Road, IAENG Secretariat, International Association of Engine, Hong Kong, Hong Kong SAR

    Sio-Iong Ao

  3. Faculty of Information Sciences and Engineering, University of Canberra, Canberra, Aust Capital Terr, Australia

    Xu Huang

  4. Calzada Tecnologico s/n, Instituto Tecnologico de Tijuana, Tijuana, Baja California, Mexico

    Oscar Castillo

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Zarea, S.A., El-Sayed, S.M., Al-Marshdy, A.A.S. (2015). Iterative Algorithms for the Linear Matrix Equation X + A*XA = I and Some Properties. In: Yang, GC., Ao, SI., Huang, X., Castillo, O. (eds) Transactions on Engineering Technologies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9588-3_8

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  • DOI: https://doi.org/10.1007/978-94-017-9588-3_8

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