论文标题
最佳收敛速率的理性光谱过滤器
Rational spectral filters with optimal convergence rate
论文作者
论文摘要
近年来，基于轮廓的本素层已成为解决大而稀疏的特征值问题的标准方法。基于最近通过非线性正方形优化所谓的理性过滤器的最低性能的改进，我们引入了一种系统的方法来设计这些过滤器，以最大程度地降低最差的案例收敛率并消除对重量函数的参数依赖性。此外，我们提供了一种有效的方法来处理盒子构成，这些方法对于在基于轮廓的eigensolvers中使用迭代线性求解器起着核心作用。实际上，这些无参数过滤器一致地最大程度地减少了迭代次数的数量和触发器的数量，以达到本ensolver中的收敛性。作为副产品，我们的理性过滤器允许使用简单的解决方案来负载平衡，当通过切片在频谱间隔中切片来接近内部本征征的解决方案。
In recent years, contour-based eigensolvers have emerged as a standard approach for the solution of large and sparse eigenvalue problems. Building upon recent performance improvements through non-linear least square optimization of so-called rational filters, we introduce a systematic method to design these filters by minimizing the worst-case convergence ratio and eliminate the parametric dependence on weight functions. Further, we provide an efficient way to deal with the box-constraints which play a central role for the use of iterative linear solvers in contour-based eigensolvers. Indeed, these parameter-free filters consistently minimize the number of iterations and the number of FLOPs to reach convergence in the eigensolver. As a byproduct, our rational filters allow for a simple solution to load balancing when the solution of an interior eigenproblem is approached by the slicing of the sought after spectral interval.
