Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
Mathematics of Computation
Matrix computations (3rd ed.)
A refined subspace iteration algorithm for large sparse eigenproblems
Applied Numerical Mathematics
ACM Transactions on Mathematical Software (TOMS)
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
An analysis of the Rayleigh—Ritz method for approximating eigenspaces
Mathematics of Computation
Matrix algorithms
GMRES with Deflated Restarting
SIAM Journal on Scientific Computing
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
A Test Matrix Collection for Non-Hermitian Eigenvalue Problems
A Test Matrix Collection for Non-Hermitian Eigenvalue Problems
A modified harmonic block Arnoldi algorithm with adaptive shifts for large interior eigenproblems
Journal of Computational and Applied Mathematics
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method
ACM Transactions on Mathematical Software (TOMS)
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The block Arnoldi method is one of the most commonly used techniques for large eigenproblems. In this paper, we exploit certain modified Ritz vectors to take the place of Ritz vectors in the thick-restarted block Arnoldi algorithm, and propose a modified thick-restarted block Arnoldi algorithm for large eigenproblems. We then consider how to periodically combine the refined subspace iterative method with the modified thick-restarting block Arnoldi algorithm for computing a few dominant eigenpairs of a large matrix. The resulting algorithm is called a Subspace-Block Arnoldi algorithm. Numerical experiments show the efficiency of our new algorithms.