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Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for M-matrices. (English) Zbl 0996.65047
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.

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
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