Juang J, Lin W W. Nonsymmetric algebraic Riccati equations and Hamiltonian-like matrices[J]. SIAM J. Matrix Anal. Appl., 1999, 20: 228-243.
[2]
Juang J. Existence of algebraic matrix Riccati equations arising in transport theory[J]. Linear Algebra Appl., 1995, 230: 89-100.
[3]
Lu L Z. Solution form and simple iteration of a nonsymmetric algebraic Riccati equation arising in transport theory[J]. SIAM J. Matrix Anal. Appl., 2005, 26: 679-685.
[4]
Guo C H, Laub A J. On the iterative solution of a class of nonsymmetric algebraic Riccati equations[J]. SIAM J. Matrix Anal. Appl., 2000, 22: 376-391.
[5]
Bao L, Lin Y, Wei Y. A modified simple iterative method for nonsymmetric algebraic Riccati equations arising in transport theory[J]. Appl. Math. Comput., 2006, 181: 1499-1504.
[6]
Bai Z Z, Gao Y H, Lu L Z. Fast iterative schemes for nonsymmetric algebraic Riccati equations arising from transport theory[J]. SIAM J. Sci. Comput., 2008, 30: 804-818.
[7]
C.H. Guo, Lin W W. Convergence rates of some iterative methods for nonsymmetric algebraic Riccati equations arising in transport theory[J]. Linear Algebra Appl., 2010, 432: 283-291.
[8]
Wu S, Huang C. Two-step relaxation Newton method for nonsymmetric algebraic Riccati equations arising from transport theory[J]. Math. Probl. Eng., 2009, 12: 1-17.
[9]
Lin Y. A class of iterative methods for solving nonsymmetric algebraic Riccati equations arising in transport theory[J]. Comput. Math. Appl., 2008, 56: 3046-3051.
[10]
Lin Y, Bao L, Wu Q. On the convergence rate of an iterative method for solving nonsymmetric algebraic Riccati equations[J]. Comput. Math. Appl., 2011, 62: 4178-4184.
[11]
Berman A, Plemmons R J. Nonnegative matrices in the mathematical sciences, Academic Press, New York, 1979.
[12]
Fiedler M, Ptak V. On matrices with non-positive off-diagonal elements and positive principal minors[J]. Czechoslovak Math. J., 1962, 12: 382-400.
[13]
Bini D A, Meini B and Poloni F. From algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms, Proceeding of Numerical Methods for Structured Markov Chains, Dagstuhl Seminar Proceedings, IBFI, Schloss Dagstuhl, Germany 2008.
[14]
Bini D A, Meini B and Poloni F. Fast solution of a certain Riccati equation through Cauchy-like matrices[J]. Electron. Trans. Numer. Anal., 2009, 33: 84-104.
[15]
Gao Y H and Bai Z Z. On inexact Newton methods based on doubling iteration scheme for nonsymmetric algebraic Riccati equations[J]. Numer. Linear Algebra Appl., 2011, 18: 325-341.
[16]
Guo C H. Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for Mmatrices[J]. SIAM J. Matrix Anal. Appl., 2001, 23: 225-242.
[17]
Guo X X, Lin W W and Xu S F. A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation[J]. Numer. Math., 2006, 103: 393-412.
[18]
Juang J and Chen I D. Iterative solution for a certain class of algebraic matrix Riccati equations arising in transport theory[J]. Tansport Theory Statist. Phys., 1993, 22: 65-80.
[19]
Juang J and Lin Z T. Convergence of an iterative technique for algebraic matrix Riccati euqations and applications to transport theory[J]. Tansport Theory Statist. Phys., 1992, 21: 87-100.
[20]
Bai Z Z, Guo X X and Xu S F. Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations[J]. Numer. Linear Algebra Appl., 2006, 13: 655-674.
[21]
Benner P, Mena H and Saak J. On the parameter selection problem in the Newton-ADI iteration for large-scale Riccati equations[J]. Electr. Trans. Num. Anal., 2008, 29: 136-149.
[22]
Benner P and Saak J. A Galerkin-Newton-ADI method for solving largescale algebraic Riccati equations, Preprint SPP1253-090, DFG Priority Programme Optimization with Partial Differential Equations, (2010) . URL http:././www.am.unierlangen.de./ home./spp1253./wiki./index.php./Preprints
[23]
Bini D A, Iannazzo B and Poloni F. A fast Newton's method for a nonsymmetric algebraic Riccati equation[J]. SIAM J. Matrix Anal. Appl., 2008, 30: 276-290.
[24]
Guo C H, Iannazzo B and Meini B. On the doubling algorithm for a (shifted) nonsymmetric algebraic Riccati equations[J]. SIAM J. Matrix Anal. Appl., 2007, 29: 1083-1100.
[25]
Lu L Z. Newton iterations for a nonsymmetric algebraic Riccati equation[J]. Numer. Linear Algebra Appl., 2005, 12: 191-200.
[26]
Li J R and White J. Low-rank solution of Lyapunov equations[J]. SIAM J. Matrix Anal. Appl., 2002, 24: 260-280.
[27]
Martinsson P G, Rokhlin V and Tygert M. A fast algorithm for the inversion of general Toeplitz matrices[J]. Comput. Math. Appl., 2005, 50: 741-752.
[28]
Penzl T. A cyclic low-rank smith method for large sparse Lyapunov equations[J]. SIAM J. Sci. Comput., 2000, 21: 1401-1418.
[29]
Wachspress E L. Optimum alternating-direction-implicit iteration parameters for a model problem[J]. J. Soc. Indust. Appl. Math., 1962, 10: 339-350.
[30]
Wachspress E L. ADI iteration parameters for solving Lyapunov and Sylvester equations, Note of private communication, 2009.
[31]
Bai Z Z. On Hermitian and skew-Hermitian splitting iteration methods for continuous Sylvester equations[J]. J. Comp. Math., 2011, 29: 185-198.
[32]
Bai Z Z, Golub G H and Ng M K. Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems[J]. SIAM J. Matrix Anal. Appl., 2003, 24: 603-626.
