A new class of nonsymmetric algebraic Riccati equations

@article{Guo2007ANC,
  title={A new class of nonsymmetric algebraic Riccati equations},
  author={Chun-Hua Guo},
  journal={Linear Algebra and its Applications},
  year={2007},
  volume={426},
  pages={636-649}
}
  • Chun-Hua Guo
  • Published 15 October 2007
  • Mathematics
  • Linear Algebra and its Applications

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References

SHOWING 1-10 OF 25 REFERENCES

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

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

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

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

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

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

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.

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

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.