## 36 Citations

### A Parameterized Class of Complex Nonsymmetric Algebraic Riccati Equations

- MathematicsNumerical Mathematics: Theory, Methods and Applications
- 2021

In this paper, by introducing a definition of parameterized comparison matrix of a given complex square matrix, the solvability of a parameterized class of complex nonsymmetric algebraic Riccati…

### Nonsymmetric algebraic Riccati theory: A matrix pencil approach

- MathematicsProceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference
- 2009

The results may be applied in the framework of game theory to design Nash and Stackelberg strategies without the classical invertibility assumption on the direct feed-through matrix coefficient.

### General Matrix Pencil Techniques for Solving Discrete-Time Nonsymmetric Algebraic Riccati Equations

- MathematicsSIAM J. Matrix Anal. Appl.
- 2009

The theory is applied in the framework of game theory with an open-loop information structure to design Nash strategy without the classical assumptions on the invertibility of some matrix coefficients.

### A new class of complex nonsymmetric algebraic Riccati equations with its ω-comparison matrix being an irreducible singular M-matrix

- MathematicsInt. J. Comput. Math.
- 2021

A new class of complex nonsymmetric algebraic Riccati equations (NAREs) whose four coefficient matrices form a matrix with its ω-comparison matrix being an irreducible singular M-matrix is presented.

### Nonsymmetric algebraic Riccati equations

- Computer Science
- 2011

The research activity concerning the analysis of nonsymmetric algebraic Riccati equations associated with M-matrices and the design of numerical algorithms for their solution has had a strong…

### Exact line search method for solving nonsymmetric algebraic riccati equations arising from open-loop linear quadratic differential games

- Mathematics2016 International Conference on Instrumentation, Control and Automation (ICA)
- 2016

We consider a set of coupled algebraic Riccati equations arising from non-cooperative open-loop linear quadratic differential games for infinite-planning horizon and two-player case. Such coupled…

### A class of complex nonsymmetric algebraic Riccati equations associated with H-matrix

- Mathematics, Computer ScienceJ. Comput. Appl. Math.
- 2020

### From Algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms

- Computer ScienceNumerical Methods for Structured Markov Chains
- 2007

The problem of reducing an algebraic Riccati equation $XCX-AX-XD+B=0$ to a unilateral quadratic matrix equation (UQME) of the
kind $PX^2+QX+R$ is analyzed. New reductions are introduced
which…

### A new linearized implicit iteration method for nonsymmetric algebraic Riccati equations

- Mathematics
- 2016

For the nonsymmetric algebraic Riccati equation, we establish a new linearized implicit iteration method (LI) for computing its minimal nonnegative solution. And a modified linearized implicit…

### A new linearized implicit iteration method for nonsymmetric algebraic Riccati equations

- MathematicsJournal of Applied Mathematics and Computing
- 2015

For the nonsymmetric algebraic Riccati equation, we establish a new linearized implicit iteration method (LI) for computing its minimal nonnegative solution. And a modified linearized implicit…

## References

SHOWING 1-10 OF 25 REFERENCES

### On the Iterative Solution of a Class of Nonsymmetric Algebraic Riccati Equations

- MathematicsSIAM J. Matrix Anal. Appl.
- 2000

Newton's method and a class of basic fixed-point iterations can be used to find its minimal positive solution whenever it has a positive solution of any equation in this class of nonsymmetric algebraic Riccati equations.

### ON THE MINIMAL NONNEGATIVE SOLUTION OFNONSYMMETRIC ALGEBRAIC RICCATI EQUATION

- Mathematics, Computer Science
- 2005

Using the matrix sign function method, it is shown how to compute the desired M-matrix solution of the quadratic matrix equation X^2 - EX - F = 0 by connecting it with the nonsymmetric algebraic Riccati equation, where E is a diagonal matrix and F is an M- matrix.

### Nonsymmetric Algebraic Riccati Equations and Wiener-Hopf Factorization for M-Matrices

- MathematicsSIAM J. Matrix Anal. Appl.
- 2001

It is explained how the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M-matrix can be found by the Schur method and compared with Newton's method and basic fixed-point iterations.

### Iterative solution of algebraic matrix Riccati equations in open loop Nash games

- Mathematics
- 2003

In this note we study a fixed point iteration approach to solve algebraic Riccati equations as they appear in general two player Nash differential games on an infinite time horizon, where the…

### Nonsymmetric Algebraic Riccati Equations and Hamiltonian-like Matrices

- MathematicsSIAM J. Matrix Anal. Appl.
- 1998

We consider a nonsymmetric algebraic matrix Riccati equation arising from transport theory. The nonnegative solutions of the equation can be explicitly constructed via the inversion formula of a…

### A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation

- Mathematics, Computer ScienceNumerische Mathematik
- 2006

A structure-preserving doubling algorithm for the computation of the minimal nonnegative solution to the nonsymmetric algebraic Riccati equation (NARE), based on the techniques developed for the symmetric cases, which outperforms Newton's iteration and the fixed-point iteration methods.

### A note on the minimal nonnegative solution of a nonsymmetric algebraic Riccati equation

- Mathematics
- 2002

### On the solution of algebraic Riccati equations arising in fluid queues

- Mathematics, Computer Science
- 2006

### On the Doubling Algorithm for a (Shifted) Nonsymmetric Algebraic Riccati Equation

- MathematicsSIAM J. Matrix Anal. Appl.
- 2007

Nonsymmetric algebraic Riccati equations for which the four coefficient matrices form an irreducible singular $M$-matrix, which arises in the study of Markov models, are considered.