Guo, Chun-Hua Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for M-matrices. (English) Zbl 0996.65047 SIAM J. Matrix Anal. Appl. 23, No. 1, 225-242 (2001). The nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M-matrix is considered. Several iterative methods are discussed. A new sufficient condition for the existence of a nonnegative solution is obtained. This condition is closely related to the Wiener-Hopf factorization for M-matrices. It is illustrated how the minimal nonnegative solution can be found by the Schur method. Numerical examples are presented to compare the Schur method with Newton’s method and some fixed-point iterations. Reviewer: Liu Xinguo (Qingdao) Cited in 85 Documents MSC: 65F30 Other matrix algorithms (MSC2010) 15A24 Matrix equations and identities 65H10 Numerical computation of solutions to systems of equations 15B48 Positive matrices and their generalizations; cones of matrices Keywords:nonsymmetric algebraic Riccati equations; M-matrices; Wiener-Hopf factorization; minimal nonnegative solution; Schur method; Newton’s method; fixed-point iterations; comparison of methods; numerical examples; iterative methods PDFBibTeX XMLCite \textit{C.-H. Guo}, SIAM J. Matrix Anal. Appl. 23, No. 1, 225--242 (2001; Zbl 0996.65047) Full Text: DOI