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

  • Sana’a A. Zarea
  • Salah M. El-Sayed
  • Amal A. S. Al-Marshdy
Chapter

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.

Keywords

Algorithm Fixed point iteration Linear matrix equation Numerical analysis Positive definite solutions Properties Two sided iteration 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Sana’a A. Zarea
    • 1
  • Salah M. El-Sayed
    • 2
  • Amal A. S. Al-Marshdy
    • 3
  1. 1.Princess Nourah Bint Abdulrahman UniversityRiyadKSA
  2. 2.Benha UniversityBenhaEgypt
  3. 3.Hail UniversityHailKSA

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