  We consider the algebraic Riccati equation for which the four coefficient
matrices form an M-matrix K. When K is a nonsingular M-matrix or an irreducible
singular M-matrix, the Riccati equation is known to have a minimal nonnegative
solution and several efficient methods are available to find this solution. In
this paper we are mainly interested in the case where K is a reducible singular
M-matrix. Under a regularity assumption on the M-matrix K, we show that the
Riccati equation still has a minimal nonnegative solution. We also study the
properties of this particular solution and explain how the solution can be
found by existing methods.

Numerical Analysis