【摘要】 符号函数是求解来自控制论中相关的Lyapunov方程和Riccati方程的有力工具,它也用来解某些特征值问题和计算不变子空间.本文给出了求矩阵符号函数的割线法,证明了该方法对于特殊的初始矩阵是全局超线性收敛的,并给出了数值试验,并将割线法与Newton法进行了比较,理论上和数值上均验证了割线法是求矩阵符号函数的有效数值方法.更多还原

【Abstract】 The sign function is a useful tool for solving the Lyapunov and the Riccati equation which arise from problems related to control theory.It is also used to solve some eigenvalue problems and to compute invariant subspaces.In this paper,a secant method is proposed to compute the sign function of a given matrix.The global and superlinear convergence of the method is proved under specifically initialized matrices.The numerical examples are also provided.And a comparison is done between the secant method and the Newton method.It is shown that the secant method is an effective numerical method to compute the sign function theoretically and empirically.更多还原