The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software
The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software
复制标题
特征值切片库 (EVSL)：算法、实现和软件
DOI：
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发表时间：
2018
影响因子：
3.1
通讯作者：
Y. Saad
中科院分区：
文献类型：
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作者：
Ruipeng Li;Yuanzhe Xi;Lucas Erlandson;Y. Saad
本文介绍了一个求解大型稀疏真实的对称标准和广义特征值问题的软件包EVSL（for EigenValues Slicing Library）。正如它的名字所示，该软件包利用频谱切片，一种将频谱划分为许多子区间并从每个子区间独立提取特征对的策略。为了实现这样的策略，在EVSL中实现的方法依赖于给定矩阵或矩阵对的谱密度的快速计算。EVSL与其他现有软件包的区别在于EVSL完全依赖于过滤技术。多项式和有理滤波都实现，并与Krylov子空间方法和子空间迭代算法相结合。在实现方面，该软件包为各种场景提供了接口，包括无矩阵模式，用户可以提供自己的函数来执行矩阵向量运算或求解稀疏线性系统。本文介绍了EVSL中的算法，提供了它们的实现细节，并讨论了各种方法的性能问题。
This paper describes a software package called EVSL (for EigenValues Slicing Library) for solving large sparse real symmetric standard and generalized eigenvalue problems. As its name indicates, the package exploits spectrum slicing, a strategy that consists of dividing the spectrum into a number of subintervals and extracting eigenpairs from each subinterval independently. In order to enable such a strategy, the methods implemented in EVSL rely on a quick calculation of the spectral density of a given matrix, or a matrix pair. What distinguishes EVSL from other currently available packages is that EVSL relies entirely on filtering techniques. Polynomial and rational filtering are both implemented and are coupled with Krylov subspace methods and the subspace iteration algorithm. On the implementation side, the package offers interfaces for various scenarios including matrix-free modes, whereby the user can supply his/her own functions to perform matrix-vector operations or to solve sparse linear systems. The paper describes the algorithms in EVSL, provides details on their implementations, and discusses performance issues for the various methods.