二阶系统数值解耦方法的研究

数值代数领域通过保持Lancaster结构来研究二阶系统的解耦问题,但寻找解耦变换涉及到了非线性方程组求解问题,难以实现. 提出了一种二阶系统数值解耦的新方法. 根据系统解耦前后的同谱信息确定解耦后的系统,将寻找解耦变换的非线性问题转化为齐次Sylvester方程求解问题; 并利用矩阵的Kronecker积理论求解二阶系统的解耦变换. 数值试验证明了该方法的可行性,为二阶系统的数值解耦找到了更便易的实现途径.

Numerical decoupling of quadratic system

In numerical algebra field, the quadratic system decoupling is researched by preserving Lancaster structure, but it is difficult to find decoupling transformations, which involves the solution of nonlinear equations. A new method of numerical decoupling of quadratic system is proposed in this paper. The decoupled system is identified by the isospectrality of systems, and the nonlinear problem to solve decoupling transformations is converted to the solution of Sylvester equation. The decoupling transformations are given based on the Kronecker product knowledge of matrixes. The method is shown to be feasible by numerical experiments, and it supplies a new point for quadratic system decoupling research.