Abstract
We consider the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M-matrix. Nonsymmetric algebraic Riccati equations of this type appear in applied probability and transport theory. The minimal nonnegative solution of these equations can be found by Newton's method and basic fixed-point iterations. The study of these equations is also closely related to the so-called Wiener--Hopf factorization for M-matrices. We explain how the minimal nonnegative solution can be found by the Schur method and compare the Schur method with Newton's method and some basic fixed-point iterations. The development in this paper parallels that for symmetric algebraic Riccati equations arising in linear quadratic control.
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