Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
Mathematics of Computation
Applied numerical linear algebra
Applied numerical linear algebra
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
Parallel empirical pseudopotential electronic structure calculations for million atom systems
Journal of Computational Physics
Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems
Journal of Computational Physics
A thick-restarted block Arnoldi algorithm with modified Ritz vectors for large eigenproblems
Computers & Mathematics with Applications
A communication-avoiding thick-restart lanczos method on a distributed-memory system
Euro-Par'11 Proceedings of the 2011 international conference on Parallel Processing
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The Thick-Restart Lanczos (TRLan) method is an effective method for solving large-scale Hermitian eigenvalue problems. The performance of the method strongly depends on the dimension of the projection subspace used at each restart. In this article, we propose an objective function to quantify the effectiveness of the selection of subspace dimension, and then introduce an adaptive scheme to dynamically select the dimension to optimize the performance. We have developed an open-source software package a--TRLan to include this adaptive scheme in the TRLan method. When applied to calculate the electronic structure of quantum dots, a--TRLan runs up to 2.3x faster than a state-of-the-art preconditioned conjugate gradient eigensolver.