Existence of algebraic matrix Riccati equations arising in transport theory
@article{Juang1995ExistenceOA,
title={Existence of algebraic matrix Riccati equations arising in transport theory},
author={Jonq Juang},
journal={Linear Algebra and its Applications},
year={1995},
volume={230},
pages={89-100}
}87 Citations
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.
Solution Form and Simple Iteration of a Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory
- Mathematics, Computer ScienceSIAM J. Matrix Anal. Appl.
- 2005
It is shown that this computation can be done via computing only the minimal positive solution of a vector equation, which is derived from the special form of solutions of the Riccati equation.
A class of iterative methods for solving nonsymmetric algebraic Riccati equations arising in transport theory
- MathematicsComput. Math. Appl.
- 2008
Fast verified computation for solutions of algebraic Riccati equations arising in transport theory
- MathematicsNumer. Linear Algebra Appl.
- 2017
A fast algorithm for enclosing the solution of the nonsymmetric algebraic Riccati equation arising in transport theory is proposed, which verifies the uniqueness and minimal positiveness of the enclosed solution.
Explicit Solutions for a Riccati Equation from Transport Theory
- MathematicsSIAM J. Matrix Anal. Appl.
- 2008
Formulas for the minimal positive solution of a particular nonsymmetric Riccati equation arising in transport theory are derived based on the eigenvalues of an associated matrix to derive fast and highly accurate numerical methods.
Numerical Study on Nonsymmetric Algebraic Riccati Equations
- Mathematics
- 2016
In this paper, we consider the nonsymmetric algebraic Riccati equation whose four coefficient matrices form an M-matrix K. When K is a regular M-matrix, the Riccati equation is known to have a…
Numerical Study on Nonsymmetric Algebraic Riccati Equations
- MathematicsMediterranean Journal of Mathematics
- 2016
In this paper, we consider the nonsymmetric algebraic Riccati equation whose four coefficient matrices form an M-matrix K. When K is a regular M-matrix, the Riccati equation is known to have a…
A modified structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equations from transport theory
- MathematicsJ. Comput. Appl. Math.
- 2014
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