Some accelerated iterative algorithms for solving nonsymmetric algebraic Riccati equations arising in transport theory

Abstract

In this paper, some accelerated iterative algorithms are developed to find the minimal positive solution of the nonsymmetric algebraic Riccati equation arising in transport theory. The convergence analysis shows that the sequences of vectors generated by iterative algorithms with the initial vector $(e,e)$ are monotonically increasing and converge to the minimal positive solution of the vector equations. Numerical examples are provided to illustrate the efficiency of the proposed algorithms and testify the conclusions suggested in this paper.

Keywords:

• Nonsymmetric algebraic Riccati equation
• minimal positive solution
• accelerated iterative algorithm
• convergence analysis

2010 Mathematics Subject Classifications:

• 65H10
• 15A24

Acknowledgments

The authors deeply thank the anonymous referees for helping to improve the original manuscript by valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Key Research and Development Program of China (2018YFC1504200, 2018YFC0603500) and National Science Foundation of China(11901098).