Generalizations of Davidson's method for computing eigenvalues of sparse symmetric matrices
SIAM Journal on Scientific and Statistical Computing
A multilevel variational method for Au= Bu on composite Grids
Journal of Computational Physics
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
SIAM Journal on Matrix Analysis and Applications
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
A Truncated RQ Iteration for Large Scale Eigenvalue Calculations
SIAM Journal on Matrix Analysis and Applications
Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
SIAM Journal on Scientific Computing
Thick-restart Lanczos method for electronic structure calculations
Journal of Computational Physics
Parallel methods and tools for predicting material properties
Computing in Science and Engineering
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Matrix algorithms
SIAM Journal on Scientific Computing
Implicitly Restarted Arnoldi Methods and Subspace Iteration
SIAM Journal on Matrix Analysis and Applications
A Krylov--Schur Algorithm for Large Eigenproblems
SIAM Journal on Matrix Analysis and Applications
Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
IRBL: An Implicitly Restarted Block-Lanczos Method for Large-Scale Hermitian Eigenproblems
SIAM Journal on Scientific Computing
ACM Transactions on Mathematical Software (TOMS)
Self-consistent-field calculations using Chebyshev-filtered subspace iteration
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A Chebyshev-Davidson Algorithm for Large Symmetric Eigenproblems
SIAM Journal on Matrix Analysis and Applications
State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems
Journal of Computational Physics
Practical acceleration for computing the HITS ExpertRank vectors
Journal of Computational and Applied Mathematics
Dissecting the FEAST algorithm for generalized eigenproblems
Journal of Computational and Applied Mathematics
Hi-index | 31.45 |
We propose a block Davidson-type subspace iteration using Chebyshev polynomial filters for large symmetric/hermitian eigenvalue problem. The method consists of three essential components. The first is an adaptive procedure for constructing efficient block Chebyshev polynomial filters; the second is an inner-outer restart technique inside a Chebyshev-Davidson iteration that reduces the computational costs related to using a large dimension subspace; and the third is a progressive filtering technique, which can fully employ a large number of good initial vectors if they are available, without using a large block size. Numerical experiments on several Hamiltonian matrices from density functional theory calculations show the efficiency and robustness of the proposed method.