HARP: a fast spectral partitioner
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
A Comparison of Factorization-Free Eigensolvers with Application to Cavity Resonators
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Sourcebook of parallel computing
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Sparsity: Optimization Framework for Sparse Matrix Kernels
International Journal of High Performance Computing Applications
SIPs: Shift-and-invert parallel spectral transformations
ACM Transactions on Mathematical Software (TOMS)
A modified harmonic block Arnoldi algorithm with adaptive shifts for large interior eigenproblems
Journal of Computational and Applied Mathematics
Accelerated subspace iteration with aggressive shift
Computers and Structures
Parallel computation of the eigenvalues of symmetric Toeplitz matrices through iterative methods
Journal of Parallel and Distributed Computing
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
PRIMME: preconditioned iterative multimethod eigensolver—methods and software description
ACM Transactions on Mathematical Software (TOMS)
Deflated block Krylov subspace methods for large scale eigenvalue problems
Journal of Computational and Applied Mathematics
Time-memory trade-offs using sparse matrix methods for large-scale eigenvalue problems
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
VECPAR'06 Proceedings of the 7th international conference on High performance computing for computational science
Fast eigenvalue calculations in a massively parallel plasma turbulence code
Parallel Computing
Efficient buckling and free vibration analysis of cyclically repeated space truss structures
Finite Elements in Analysis and Design
A block Chebyshev-Davidson method with inner-outer restart for large eigenvalue problems
Journal of Computational Physics
Implementation and tuning of a parallel symmetric Toeplitz eigensolver
Journal of Parallel and Distributed Computing
The Lanczos Method for Parameterized Symmetric Linear Systems with Multiple Right-Hand Sides
SIAM Journal on Matrix Analysis and Applications
Algebraic sub-structuring for electromagnetic applications
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Strategies for spectrum slicing based on restarted Lanczos methods
Numerical Algorithms
Improving eigenpairs of automated multilevel substructuring with subspace iterations
Computers and Structures
A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh
Journal of Computational Physics
| Hi-index | 0.01 |
An "industrial strength" algorithm for solving sparse symmetric generalized eigenproblems is described. The algorithm has its foundations in known techniques in solving sparse symmetric eigenproblems, notably the spectral transformation of Ericsson and Ruhe and the block Lanczos algorithm. However, the combination of these two techniques is not trivial; there are many pitfalls awaiting the unwary implementor. The focus of this paper is on identifying those pitfalls and avoiding them, leading to a "bomb-proof" algorithm that can live as a black box eigensolver inside a large applications code. The code that results comprises a robust shift selection strategy and a block Lanczos algorithm that is a novel combination of new techniques and extensions of old techniques.