Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Block algorithms for reordering standard and generalized Schur forms
ACM Transactions on Mathematical Software (TOMS)
Parallel Eigensolvers for a Discretized Radiative Transfer Problem
High Performance Computing for Computational Science - VECPAR 2008
Anasazi software for the numerical solution of large-scale eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Fast eigenvalue calculations in a massively parallel plasma turbulence code
Parallel Computing
Preconditioning bandgap eigenvalue problems in three-dimensional photonic crystals simulations
Journal of Computational Physics
A block Chebyshev-Davidson method with inner-outer restart for large eigenvalue problems
Journal of Computational Physics
Efficient Arnoldi-type algorithms for rational eigenvalue problems arising in fluid-solid systems
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Strategies for spectrum slicing based on restarted Lanczos methods
Numerical Algorithms
Eigenvalue computations in the context of data-sparse approximations of integral operators
Journal of Computational and Applied Mathematics
Efficient evaluation of the direct and adjoint linearized dynamics from compressible flow solvers
Journal of Computational Physics
Numerical studies on structure-preserving algorithms for surface acoustic wave simulations
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Matrix-free continuation of limit cycles for bifurcation analysis of large thermoacoustic systems
Journal of Computational Physics
Fast nonrigid 3D retrieval using modal space transform
Proceedings of the 3rd ACM conference on International conference on multimedia retrieval
Journal of Scientific Computing
Journal of Computational Physics
Scalable matrix computations on large scale-free graphs using 2D graph partitioning
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh
Journal of Computational Physics
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Sorensen's implicitly restarted Arnoldi algorithm is one of the most successful and flexible methods for finding a few eigenpairs of a large matrix. However, the need to preserve the structure of the Arnoldi decomposition on which the algorithm is based restricts the range of transformations that can be performed on the decomposition. In consequence, it is difficult to deflate converged Ritz vectors from the decomposition. Moreover, the potential forward instability of the implicit QR algorithm can cause unwanted Ritz vectors to persist in the computation. In this paper we introduce a general Krylov decomposition that solves both problems in a natural and efficient manner.