广义特征值摄动问题的逐步逼近法

A Successive Approximation Procedure for the Generalized Eigenvalue Perturbation Problem

以子空间缩聚及正交分解为基础，根据实矩阵的奇异值分解定理，对广义特征值摄动问题，提出了一种能同时有效地处理孤立特征值、相重特征值及相近特征值三种不同情况的逐步逼近法．计算实例表明，该方法合理可靠。

For the generalized eigenvalue perturbation problem of real modes, an efficient method is put forward, which is applicable to all the three cases of eigenvalue problems: distinct, repeated and nearly equal eigenvalues. This method is a kind of successive approximation procedure, developed by performing an orthogonal decomposition and a sub space condensation and by using the singular value decomposition of real matrix. Some illustrative examples are presented to demonstrate the validity of this proposed technique.