Generalizations of Davidson's method for computing eigenvalues of sparse symmetric matrices
SIAM Journal on Scientific and Statistical Computing
Davidson's method and preconditioning for generalized eigenvalue problems
Journal of Computational Physics
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
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
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods
SIAM Journal on Scientific Computing
Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
SIAM Journal on Scientific Computing
Matrix algorithms
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
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
On a parallel multilevel preconditioned Maxwell eigensolver
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Block algorithms for reordering standard and generalized Schur forms
ACM Transactions on Mathematical Software (TOMS)
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in Hypre and PETSc
SIAM Journal on Scientific Computing
Anasazi software for the numerical solution of large-scale eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
A new iterative scheme for obtaining eigenvectors of large, real-symmetric matrices
Journal of Computational Physics
PRIMME: preconditioned iterative multimethod eigensolver—methods and software description
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Computing subdominant unstable modes of turbulent plasma with a parallel Jacobi–Davidson eigensolver
Concurrency and Computation: Practice & Experience
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In the context of large-scale eigenvalue problems, methods of Davidson type such as Jacobi-Davidson can be competitive with respect to other types of algorithms, especially in some particularly difficult situations such as computing interior eigenvalues or when matrix factorization is prohibitive or highly inefficient. However, these types of methods are not generally available in the form of high-quality parallel implementations, especially for the case of non-Hermitian eigenproblems. We present our implementation of various Davidson-type methods in SLEPc, the Scalable Library for Eigenvalue Problem Computations. The solvers incorporate many algorithmic variants for subspace expansion and extraction, and cover a wide range of eigenproblems including standard and generalized, Hermitian and non-Hermitian, with either real or complex arithmetic. We provide performance results on a large battery of test problems.