  The nonsymmetric T-Riccati equation is a quadratic matrix equation where the
linear part corresponds to the so-called T-Sylvester or T-Lyapunov operator
that has previously been studied in the literature. It has applications in
macroeconomics and policy dynamics. So far, it presents an unexplored problem
in numerical analysis, and both, theoretical results and computational methods,
are lacking in the literature. In this paper we provide some sufficient
conditions for the existence and uniqueness of a nonnegative minimal solution
and its efficient computation is deeply analyzed. Both the small-scale and the
large-scale setting are addressed and Newton-Kleinman-like methods are derived.
The convergence of these procedures to the minimal solution is proved and
several numerical results illustrate the computational efficiency of the
proposed methods.
