A Structure-Preserving Curve for Symplectic Pairs and Its Applications

@article{Kuo2012ASC,
  title={A Structure-Preserving Curve for Symplectic Pairs and Its Applications},
  author={Yueh-Cheng Kuo and Shih-Feng Shieh},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2012},
  volume={33},
  pages={597-616}
}
The main purpose of this paper is the study of numerical methods for the maximal solution of the matrix equation $X+A^*X^{-1}A = Q$, where $Q$ is Hermitian positive definite. We construct a smooth curve parameterized by $t\ge 1$ of symplectic pairs with a special structure, in which the curve passes through all iteration points generated by the known numerical methods, including the fixed-point iteration, the structure-preserving doubling algorithm (SDA), and Newton's method provided that $A^*Q… 

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