解广义特征值问题的半分法

The Semidefinite Metbod of Solving the Generalized Eigenvalue Problem

本文提出了一个解广义特征值问题的方法,即用半分法确定近似特征值,用改进的Rayleigh商迭代校正近似特征值,同时求出相应的特征向量。理论证明它是一个收敛的方法。

An algorithm of solving the generalized symmetric eigenvalue problem Ax=λBx (B is nearly singular or positive semidefinite) is presented. Firstly, the approximate eigenvalue is determined by the semidefinite method. Then, the approximate eigenvalue is corrected by using the modified Rayleigh quotient iteration and the corresponding eigenvector is obtained. The convergence of this algorithm is proved.