大型陀螺特征值问题的一个高效算法

AN EFFICIENT ALGORITHM FOR LARGE GYROSCOPIC EIGENVALUE PROBLEMS

提出了求解大型广义陀螺特征值问题的一个高效算法。先通过平面镜象变换，把Ｎ阶反对称阵化为ｎ阶三对角形式的反对称阵，再利用这个特殊形式的反对称阵，把问题化为［ｎ／２］阶的三对角正定对称阵的普通特征值问题，大大节约了算机容量和运算时间。计算实例证实了本方法的快速和高效性。

A new efficient algorithm for solving large gyroscopic eigenvalue problems is developed.By using successive n 2 plane mirror transformations(Housholder transformation),the n×n inverse symmetric matrix is transformed into a n×n tridiagonal inverse symmetric matrix.By taking advantage of the special property of the tridiagonal inverse symmetric matrix,the n order gyroscopic eigenvalue problem is reduced to a -order standard eigenvalue problem for a × tridiagonal positive definite symmetric matrix,which can be solved by the existing standard programs.The presented method not only reduces greatly the order of the eigenvalue problem,but also saves the computational cost.The examples given show the high efficiency of the present method.