辛约化法求解Hamiltonian矩阵特征问题

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,采用了辛相似变换,利用辛约化法求解了Hamiltonian矩阵特征值问题,其Hamilton结构得到了充分保证,这样从根本上确保了特征值的正确性,该文提供的辛方法具有较强的有效性和可靠性。

Symplectic square reduced method for solving Hamiltonian matrix eigenvalue

To solve the exact solution of the algebraic eigenvalue problem is a difficulty although the problem seems very simple and the basic principle is familiar to scientists. This paper deals with the eigenvalue problem of the Hamiltonian matrix which is widely studied in many fields. The symplectic square reduced method is established to solve the Hamiltonian matrix eigenvalue in the course of reducing the Hamiltonian matrix. This method works with symplectic similarity transformation in which the structure of the Hamiltonian matrices is preserved. The presented algorithm has preferable validity and stability.