论文标题
一种用于解决广义特征值问题的新的子空间迭代算法
A New Subspace Iteration Algorithm for Solving Generalized Eigenvalue Problems
论文作者
论文摘要
在许多应用中，需要解决广义特征值问题（GEP），例如振动分析，量子力学，电子结构等的数值模拟。子空间迭代是一种广泛使用的算法来解决特征值问题。为了解决广义特征值问题，最近提出了一种子空间迭代方法Chebyshev-Davidson算法。在Chebyshev-Davidson算法中，Chebyshev多项式滤波器技术已纳入子空间迭代中。在本文中，基于Chebyshev-Davidson算法，构建了一种新的子空间迭代算法。在新算法中，将Chebyshev滤镜和不精确的瑞利商迭代技术组合在一起，以扩大迭代中的子空间。振动分析问题的数值结果表明，所提出的算法的迭代和计算时间的数量远低于Chebyshev-Davidson算法和一些典型的GEP解决方案算法的数值结果。此外，与数值结果中的Chebyshev-Davidson算法相比，新算法比Chebyshev-Davidson算法更稳定和可靠。
It is needed to solve generalized eigenvalue problems (GEP) in many applications, such as the numerical simulation of vibration analysis, quantum mechanics, electronic structure, etc. The subspace iteration is a kind of widely used algorithm to solve eigenvalue problems. To solve the generalized eigenvalue problem, one kind of subspace iteration method, Chebyshev-Davidson algorithm, is proposed recently. In Chebyshev-Davidson algorithm, the Chebyshev polynomial filter technique is incorporated in the subspace iteration. In this paper, based on Chebyshev-Davidson algorithm, a new subspace iteration algorithm is constructed. In the new algorithm, the Chebyshev filter and inexact Rayleigh quotient iteration techniques are combined together to enlarge the subspace in the iteration. Numerical results of a vibration analysis problem show that the number of iteration and computing time of the proposed algorithm is much less than that of the Chebyshev-Davidson algorithm and some typical GEP solution algorithms. Furthermore, the new algorithm is more stable and reliable than the Chebyshev-Davidson algorithm in the numerical results.
