We identify a relationship between the solutions of a nonsymmetric algebraic T-Riccati equation (T-NARE) and the deflating subspaces of a palindromic matrix pencil, obtained by arranging the coefficients of the T-NARE. The interplay between T-NARE and palindromic pencils allows one to derive both theoretical properties of the solutions of the equation, and new methods for its numerical solution. In particular, we propose methods based on the (palindromic) QZ algorithm and the doubling algorithm, whose effectiveness is demonstrated by several numerical tests

翻译：我们确定了非对称代代数 T-Riccati 等式(T-NARE)解决方案与通过安排 T-NARE 系数获得的低缩缩缩缩缩缩缩的平基铅笔子空间之间的关系。 T-NARE 和 Palindromic 铅笔之间的相互作用使得人们既可以得出该等式解决方案的理论属性,也可以得出其数字解决方案的新方法。特别是,我们根据(palindromic) ⁇ ⁇ 和 倍增算法提出了方法,其有效性通过若干数值测试得到证明。