# 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…

## 2 Citations

### Structure-Preserving Flows of Symplectic Matrix Pairs

- MathematicsSIAM J. Matrix Anal. Appl.
- 2016

Its solution also preserves deflating subspaces on the whole orbit (Eigenvector-preserving property) and is governed by a Riccati differential equation (RDE) of the form $\dot{W}(t)=[-W(t),I)],$ for some suitable Hamiltonian matrix $\mathscr{H}$.

### A structure preserving flow for computing Hamiltonian matrix exponential

- Materials ScienceNumerische Mathematik
- 2019

A numerical method is developed for computing the symplectic matrix pair $$(\mathcal {M},\mathcal{L})$$ which represents e-H, which is a Hamiltonian matrix exponential.

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