Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
Reducing synchronization on the parallel Davidson method for the large sparse, eigenvalue problem
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
SIAM Journal on Matrix Analysis and Applications
Applied Numerical Mathematics
Robust preconditioning of large, sparse, symmetric eigenvalue problems
Journal of Computational and Applied Mathematics
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods
SIAM Journal on Scientific Computing
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
SIAM Journal on Scientific Computing
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
The trace minimization method for the symmetric generalized eigenvalue problem
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Large-Scale Normal Coordinate Analysis for Molecular Structures
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
SIAM Journal on Scientific Computing
Adaptive Eigenvalue Computations Using Newton's Method on the Grassmann Manifold
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
Is Jacobi--Davidson Faster than Davidson?
SIAM Journal on Matrix Analysis and Applications
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Multilevel Preconditioners Constructed From Inverse-Based ILUs
SIAM Journal on Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Anasazi software for the numerical solution of large-scale eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
A truncated-CG style method for symmetric generalized eigenvalue problems
Journal of Computational and Applied Mathematics
A parallel implementation of the Jacobi-Davidson eigensolver for unsymmetric matrices
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
A scalable eigensolver for large scale-free graphs using 2D graph partitioning
Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
Journal of Computational Physics
A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc
ACM Transactions on Mathematical Software (TOMS)
Tpetra, and the use of generic programming in scientific computing
Scientific Programming - A New Overview of the Trilinos Project --Part 1
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This article describes the PRIMME software package for solving large, sparse Hermitian standard eigenvalue problems. The difficulty and importance of these problems have increased over the years, necessitating the use of preconditioning and near optimally converging iterative methods. However, the complexity of tuning or even using such methods has kept them outside the reach of many users. Responding to this problem, we have developed PRIMME, a comprehensive package that brings state-of-the-art methods from “bleeding edge” to production, with the best possible robustness, efficiency, and a flexible, yet highly usable interface that requires minimal or no tuning. We describe (1) the PRIMME multimethod framework that implements a variety of algorithms, including the near optimal methods GD+k and JDQMR; (2) a host of algorithmic innovations and implementation techniques that endow the software with its robustness and efficiency; (3) a multilayer interface that captures our experience and addresses the needs of both expert and end users.