求实矩阵全部特征值的投影幂法

A Projected Power Method for Finding all Eigenvalues of A Real Matrix

描述了求实矩阵部分或全部特征值的投影幂法的几个迭代格式。所述方法的思想是，在幂法的迭代过程中，利用投影矩阵滤去迭代向量中已知特征向量的成份，使迭代收敛到未知特征值，以达到求出矩阵全部特征值及相应的特征向量的目的。

It is proposed that seveal iterative forms of projected power method for finding all or partial eigenvalues and associated eigenvectors of a real matrix. The idea of the method presented in this paper is that the eigenvectors corresponding to calculated eigenvalues is removed in iterative sequence of approximate eigenvalues by projected matrix in iterative procedure, so that the sequence is convergening to eigenvalues other that given dominant one.Finally, we can find all eigenvalues and corresponding eigenvectors.