# 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

## References

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Abstract The subject of this paper is the convergence properties of some iterative methods for solving a certain class of algebraic matrix Riccati equations arising in transport theory. A unified…

### Convergence of an iterative technique for algebraic Matrix Riccati equations and applications to transport theory

- Mathematics
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Abstract A monotone iterative technique is applied to a class of algebraic matrix Riccati equations that is satisfied by the reflection matrix for linear particle transport in a half-space. The…

### An introduction to invariant imbedding

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This paper presents a method for calculating Eigenvalues for Sturm-Liouville Type Systems using the Invariant Imbedding Method and Applications to Equations with Periodic Coefficients.

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Part I. Auxiliary Mathematics: 1. The Equation of Transfer 2. The H- Functions 3. Integral Operators Part II. Milne Equations: 4. Iterative Solutions 5. The Wiener-Hopf Solution 6. Solutions of the…

### Errata: Computation of the asymptotic states for linear half space kinetic problems

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Abstract A spectral numerical scheme computing the asymptotic states for linear half space problems is described in the case of a simple transport equation and the linearized Bhatnagar-Gross-Krook…

### Convergence of a certain monotone iteration in the reflection matrix for a nonmultiplying half-space

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Abstract A certain monotonically increasing nonlinear iterative procedure, first employed systematically by Shimizu and Aoki, has proven quite effective for computing the reflection matrix for a…

### An investigation of a simple transport model

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Abstract Chandrasekhar's method of solution is applied to a “simple transport model” designed to simulate a velocity shift found in kinetic theory. With the iterative evaluation of the H-like…

### Convergence acceleration for the reflection matrix in a nonmultiplying half-space

- Mathematics
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Abstract The purpose of this paper is two fold. First, we shed some light on the slow convergence behaviour of a certain iterative procedure for solving the reflection matrix in a nonmultiplying…