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}
}
  • Jonq Juang
  • Published 15 November 1995
  • Mathematics
  • Linear Algebra and its Applications

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.

Solution Form and Simple Iteration of a Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory

  • Linzhang Lu
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    SIAM 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.

Fast verified computation for solutions of algebraic Riccati equations arising in transport theory

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

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.

A new class of nonsymmetric algebraic Riccati equations

Numerical Study on Nonsymmetric Algebraic Riccati Equations

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

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
...

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