论文标题
大型非矩阵特征值的多级光谱指标方法
A Multilevel Spectral Indicator Method for Eigenvalues of Large Non-Hermitian Matrices
论文作者
论文摘要
最近，提出了一个新型的特征材料家族，称为光谱指标方法（SIMS）。给定复杂平面上的区域，SIMS首先通过光谱投影计算指标。该指标用于测试该区域是否包含特征值。然后对包含特征值的区域进行细分和测试。重复该过程，直到在指定的精度内确定特征值。在本文中，使用Cayley Transformation和Krylov子空间，提出了内存有效的多级特征层。与SIMS的早期版本相比，该方法使用的记忆较少，并且特别适合计算大型稀疏（非铁）矩阵的许多特征值。示出了几个例子进行演示。
Recently a novel family of eigensolvers, called spectral indicator methods (SIMs), was proposed. Given a region on the complex plane, SIMs first compute an indicator by the spectral projection. The indicator is used to test if the region contains eigenvalue(s). Then the region containing eigenvalues(s) is subdivided and tested. The procedure is repeated until the eigenvalues are identified within a specified precision. In this paper, using Cayley transformation and Krylov subspaces, a memory efficient multilevel eigensolver is proposed. The method uses less memory compared with the early versions of SIMs and is particularly suitable to compute many eigenvalues of large sparse (non-Hermitian) matrices. Several examples are presented for demonstration.
