State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems
Journal of Computational Physics
Parallel Eigensolvers for a Discretized Radiative Transfer Problem
High Performance Computing for Computational Science - VECPAR 2008
PRIMME: preconditioned iterative multimethod eigensolver—methods and software description
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
A block Chebyshev-Davidson method with inner-outer restart for large eigenvalue problems
Journal of Computational Physics
SIAM Journal on Scientific Computing
Computers & Mathematics with Applications
A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.02 |
Large, sparse, Hermitian eigenvalue problems are still some of the most computationally challenging tasks. Despite the need for a robust, nearly optimal preconditioned iterative method that can operate under severe memory limitations, no such method has surfaced as a clear winner. In this research we approach the eigenproblem from the nonlinear perspective, which helps us develop two nearly optimal methods. The first extends the recent Jacobi-Davidson conjugate gradient (JDCG) method to JDQMR, improving robustness and efficiency. The second method, generalized-Davidson+1 (GD+1), utilizes the locally optimal conjugate gradient recurrence as a restarting technique to achieve almost optimal convergence. We describe both methods within a unifying framework and provide theoretical justification for their near optimality. A choice between the most efficient of the two can be made at runtime. Our extensive experiments confirm the robustness, the near optimality, and the efficiency of our multimethod over other state-of-the-art methods.