Matrix computations (3rd ed.)
Analysis and modification of Newton's method for algebraic Riccati equations
Mathematics of Computation
Nonsymmetric Algebraic Riccati Equations and Hamiltonian-like Matrices
SIAM Journal on Matrix Analysis and Applications
Nonsymmetric Algebraic Riccati Equations and Wiener--Hopf Factorization for M-Matrices
SIAM Journal on Matrix Analysis and Applications
On the Iterative Solution of a Class of Nonsymmetric Algebraic Riccati Equations
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation
Numerische Mathematik
Journal of Computational and Applied Mathematics
Iterative Solution of a Nonsymmetric Algebraic Riccati Equation
SIAM Journal on Matrix Analysis and Applications
On the Doubling Algorithm for a (Shifted) Nonsymmetric Algebraic Riccati Equation
SIAM Journal on Matrix Analysis and Applications
On the convergence rate of an iterative method for solving nonsymmetric algebraic Riccati equations
Computers & Mathematics with Applications
Design of adaptive robust guaranteed cost controller for wind power generator
International Journal of Automation and Computing
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In this paper, we consider the nonsymmetric algebraic Riccati equation arising in transport theory. An important feature of this equation is that its minimal positive solution can be obtained via computing the minimal positive solution of a vector equation. We propose a class of iterative methods to solve the vector equation. The convergence analysis shows that the sequence of vectors generated by iterative methods with two kinds of specific iterative matrices is monotonically increasing and converges to the minimal positive solution of the vector equation. Numerical experiments show that the new methods outperform the modified simple iterative method and Newton's method.