We present a new power method to obtain solutions of eigenvalue problems. The method can determine not only the dominant or lowest eigenvalues but also all eigenvalues without the need for a deflation procedure. The method uses a functional of an operator (or a matrix) to select or filter an eigenvalue. The method can freely select a solution by varying a parameter associated to an estimate of the eigenvalue. The convergence of the method is highly dependent on how closely the parameter to the eigenvalues. In this paper, numerical results of the method are shown to be in excellent agreement with the analytical ones.

翻译：本文提出了一种求解特征值问题的新幂法。该方法不仅能确定主特征值或最小特征值，还能无需使用收缩法即可求得所有特征值。该方法利用算子（或矩阵）的一个泛函来筛选或过滤特征值。通过改变与特征值估计值相关的参数，该方法可以自由选择解。该方法的收敛性高度依赖于参数与特征值的接近程度。本文给出的数值结果表明，该方法与解析解高度吻合。