大型不正定陀螺系统本征值问题

陀螺动力系统可以导入哈密顿辛几何体系，在哈密顿陀螺系统的辛子空间迭代法的基础上提出了一种能够有效计算大型不正定哈密顿函数的陀螺系统本征值问题的算法．利用陀螺矩阵既为哈密顿矩阵而本征值又是纯虚数或零的特点，将对应哈密顿函数为负的本征值分离开来，构造出对应哈密顿函数全为正的本征值问题，利用陀螺系统的辛子空间迭代法计算出正定哈密顿矩阵的本征值，从而解决了大型不正定陀螺系统的本征值问题,算例证明,本征解收敛得很快．

Eigenvalue Problem of a Large Scale Indefinite Gyroscopic Dynamic System

Gyroscopic dynamic system can be introduced to Hamiltonian system. Based on an adjoint sympleetic subspace iteration method of Hamiltonian gyroscopic system, an adjoint symplectic subspace iteration method of indefinite Hamiltonian function gyroscopic system is proposed to solve the eigenvalue problem of indefinite Hamiltonian function gyroscopic system. The character that the eigenvalues of Hamiltonian gyroscopic system are only pure imaginary or zero is used. The eigenvalues that Hamiltonian fuction is negative can be separated so that the eigenvalue problem of positive deftnite Hamiltonian function system is presented, and an adjoint symplectic subspace iteration method of positive definite Hamiltonian function system is used to solve the separated eigenvalue problem. Therefore, the eigenvalue problem of indefinite Hamiltonian funclion gyroscopic system is solved, two numerical examples are given to demonstrate that the eigensolutions converge exactly.