Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
A new Lanczos method for electronic structure calculations
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
Journal of Computational Physics
Sourcebook of parallel computing
Numerical solutions of a master equation for protein folding kinetics
International Journal of Bioinformatics Research and Applications
Parallel solution of large-scale eigenvalue problem for master equation in protein folding dynamics
Journal of Parallel and Distributed Computing
A new method for accelerating Arnoldi algorithms for large scale eigenproblems
Mathematics and Computers in Simulation
PRIMME: preconditioned iterative multimethod eigensolver—methods and software description
ACM Transactions on Mathematical Software (TOMS)
Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Fast iterative interior eigensolver for millions of atoms
Journal of Computational Physics
A new algorithm for computing eigenpairs of matrices
Mathematical and Computer Modelling: An International Journal
An iterative method for single and vertically stacked semiconductor quantum dots simulation
Mathematical and Computer Modelling: An International Journal
Parametric dominant pole algorithm for parametric model order reduction
Journal of Computational and Applied Mathematics
A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc
ACM Transactions on Mathematical Software (TOMS)
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The Davidson method is a popular preconditioned variant of the Arnoldi method for solving large eigenvalue problems. For theoretical as well as practical reasons the two methods are often used with restarting. Frequently, information is saved through approximated eigenvectors to compensate for the convergence impairment caused by restarting. We call this scheme of retaining more eigenvectors than needed "thick restarting" and prove that thick restarted, nonpreconditioned Davidson is equivalent to the implicitly restarted Arnoldi. We also establish a relation between thick restarted Davidson and a Davidson method applied on a deflated system. The theory is used to address the question of which and how many eigenvectors to retain and motivates the development of a dynamic thick restarting scheme for the symmetric case, which can be used in both Davidson and implicit restarted Arnoldi. Several experiments demonstrate the efficiency and robustness of the scheme.