SIAM Journal on Scientific Computing, Volume 43, Issue 4, Page A2660-A2684, January 2021.
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 nonlinear least-squares optimization of so-called rational filters, we introduce a systematic method to design these filters by minimizing the worst-case convergence rate 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.

中文翻译：

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具有最佳收敛率的有理光谱滤波器

SIAM 科学计算杂志，第 43 卷，第 4 期，第 A2660-A2684 页，2021 年 1 月。
近年来，基于轮廓的特征求解器已成为解决大型稀疏特征值问题的标准方法。通过对所谓的有理滤波器进行非线性最小二乘优化，在最近的性能改进的基础上，我们引入了一种系统方法来设计这些滤波器，通过最小化最坏情况收敛率并消除对权重函数的参数依赖性。此外，我们提供了一种处理框约束的有效方法，框约束对于在基于轮廓的特征求解器中使用迭代线性求解器起着核心作用。实际上，这些无参数滤波器始终将迭代次数和 FLOP 次数降至最低，以在特征求解器中达到收敛。作为副产品，