Hamiltonian矩阵平方约化求解特征问题的辛算法

The Symplectic Algorithm Method for Solving Hamiltonian Matrix by Means of Reduction of Squared

代数特征值问题的解法长期以来一直散发着一种特殊的魅力,因为它充分地显示出所谓经典数学与实用数值分析之间的差异。特征值问题具有貌似简单的提法,而且其基本理论多年来已为人们所熟知,然而欲求其精确解就会遇到各种挑战性问题。针对在动力天文学和控制论中,有着广泛应用前景的Hamiltonian矩阵特征问题,在Hamiltonian矩阵约化过程中,采用辛相似变换,利用平方约化法求解了Hamiltonian矩阵特征值问题,其Hamilton结构得到了保证,这样从根本上确保了特征值的正确性,方法简易可行,提供的辛方法具有较强的有效性和稳定性。

The solution has been rather attractive for long to Algebra eigenvalue problem of Hamiltonian matrix since it shows the difference adequately between the classical mathematics and the numerical analysis. It seems that it is very simply to solve eigenvalue problem because its basic principles are familiar to scientists. However, the challenging problem will occur in process of solving its exact solution. the symplectic algorithm method is established to solve Hamiltonian matrix eigenvalue, which is widely studied in dynamical astronomy and cybernetics. In the course of reducing of Hamiltonian matrix, this method works with symplectic similarity transformation applied, and keeps well the structure of the Hamiltonian matrices. This algorithm finds simpleness and feasibility, and has preferable validity and stability.