Abstract
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.
Original language | English |
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Pages (from-to) | A2660-A2684 |
Number of pages | 25 |
Journal | Siam Journal on Scientific Computing |
Volume | 43 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2021 |
Externally published | Yes |
Keywords
- BFGS
- Contour-based eigensolver
- Hermitian eigenvalue problem
- Load balancing
- Nonlinear least squares
- Worst-case convergence rate