论文标题
用于聚类特征值的简单外推法
A simple extrapolation method for clustered eigenvalues
论文作者
论文摘要
本文介绍了功率方法的简单变体。在分析和数值上显示，以加速收敛到主要的特征值/特征向量对；而且，对于较小的频谱差距的问题特别有效。引入的方法是一种单步外推技术，它使用当前和先前更新步骤的线性组合来形成对主要特征向量的更好近似。提供的分析表明，该方法相对于两个最大特征值之间的比率成倍收敛，该方法在此过程中也近似。还引入了一种增强技术，并显示出可以稳定迭代的早期阶段。提供了数值示例来说明理论并证明方法。
This paper introduces a simple variant of the power method. It is shown analytically and numerically to accelerate convergence to the dominant eigenvalue/eigenvector pair; and, it is particularly effective for problems featuring a small spectral gap. The introduced method is a one-step extrapolation technique that uses a linear combination of current and previous update steps to form a better approximation of the dominant eigenvector. The provided analysis shows the method converges exponentially with respect to the ratio between the two largest eigenvalues, which is also approximated during the process. An augmented technique is also introduced, and is shown to stabilize the early stages of the iteration. Numerical examples are provided to illustrate the theory and demonstrate the methods.
