论文标题
在非对称T-Riccati方程的溶液上
On the Solution of the Nonsymmetric T-Riccati Equation
论文作者
论文摘要
非对称T-Riccati方程是二次矩阵方程，其中线性部分对应于先前在文献中已经研究过的所谓的T-Sylvester或T-Lyapunov操作员。它在宏观经济学和政策动态中具有应用。到目前为止，它在数值分析中提出了一个未开发的问题，并且在文献中都缺乏理论结果和计算方法。在本文中，我们为非负最小解决方案的存在和独特性提供了一些足够的条件，并深入分析了其有效计算。小规模和大规模设置均已解决，并得出了类似牛顿 - 克莱曼的方法。证明了这些程序与最小解决方案的收敛性，并且几个数值结果说明了所提出方法的计算效率。
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.
