论文标题
一种基于轮廓的非线性本质层的迭代方法
An Iterative Method for Contour-Based Nonlinear Eigensolvers
论文作者
论文摘要
轮廓集成技术已成为解决线性和非线性特征值问题的流行选择。它们主要包括Sakurai-Sugiura方法，Beyn的算法，盛宴/NLFEAST算法和其他合理的过滤技术。尽管这些方法可能会导致有效的“黑盒”方法来解决线性特征值问题，但它们仍然存在一些缺点，以解决非线性特征值问题，这些问题在数学上和实际上都更具挑战性。在本文中，我们引入了一种新的混合算法，该算法将NLFFEAST的迭代性质与Beyn处理一般非线性的方法相结合。这样，这种NLFeast-Beyn混合算法可以克服分别采用的两种算法的当前局限性。从BEYN和NLFEAST的角度提出其推导后，讨论了几个数值示例，以证明新技术的效率。
Contour integration techniques have become a popular choice for solving the linear and non-linear eigenvalue problems. They principally include the Sakurai-Sugiura methods, the Beyn's algorithm, the FEAST/NLFEAST algorithms and other rational filtering techniques. While these methods can result in effective 'black-box' approach for solving linear eigenvalue problems, they still present several shortcomings for addressing nonlinear eigenvalue problems which are both mathematically and practically far more challenging. In this paper, we introduce a new hybrid algorithm that advantageously combines the iterative nature of NLFEAST with the effectiveness of Beyn's approach to deal with general non-linearity. In doing so, this NLFEAST-Beyn hybrid algorithm can overcome current limitations of both algorithms taken separately. After presenting its derivation from both a Beyn's and NLFEAST's perspective, several numerical examples are discussed to demonstrate the efficiency of the new technique.
