# Solution of a nonsymmetric algebraic Riccati equation from a one-dimensional multistate transport model

@article{Li2011SolutionOA, title={Solution of a nonsymmetric algebraic Riccati equation from a one-dimensional multistate transport model}, author={Tie-xiang Li and Eric King-wah Chu and Jong Juang and Wen-Wei Lin}, journal={Ima Journal of Numerical Analysis}, year={2011}, volume={31}, pages={1453-1467} }

For the steady-state solution of a differential equation from a one-dimensional multistate model in transport theory, we shall derive and study a nonsymmetric algebraic Riccati equation B− − X F− − F+X + X B+X = 0, where F± ≡ (I − F)D± and B± ≡ B D± with positive diagonal matrices D± and possibly low-ranked matrices F and B. We prove the existence of the minimal positive solution X∗ under a set of physically reasonable assumptions and study its numerical computation by fixed-point iteration…

## 6 Citations

### Low-rank approximation to the solution of a nonsymmetric algebraic Riccati equation from transport theory

- MathematicsAppl. Math. Comput.
- 2012

### Solving Large-Scale Nonsymmetric Algebraic Riccati Equations by Doubling

- MathematicsSIAM J. Matrix Anal. Appl.
- 2013

The resulting large-scale doubling algorithm has an O(n) computational complexity and memory requirement per iteration and converges essentially quadratically.

### Doubling algorithm for the discretized Bethe-Salpeter eigenvalue problem

- Computer ScienceMath. Comput.
- 2019

The structure-preserving doubling algorithm, originally for algebraic Riccati equations, is extended for the discretized Bethe-Salpeter eigenvalue problem, and numerical results are presented to demonstrate the efficiency and structure- Preserving nature of the algorithm.

### Highly accurate decoupled doubling algorithm for large-scale M-matrix algebraic Riccati equations

- Computer ScienceArXiv
- 2020

A new doubling iteration is derived, decoupling the four original iteration formulae in the alternating-directional doubling algorithm, and it is proved that the kernels in the decoupled algorithm are small M-matrices.

### Sherman–Morrison–Woodbury formula for Sylvester and T-Sylvester equations with applications

- MathematicsInt. J. Comput. Math.
- 2013

This novel approach allows us to derive a matrix version of the Sherman–Morrison–Woodbury-type formula for the Sylvester equation as well as for the T-Sylvester equation which seems to be new.

### Solving large-scale nonsymmetric algebraic Riccati equations from two-dimensional transport models by doubling

- Computer ScienceJ. Comput. Appl. Math.
- 2021

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