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
ScaLAPACK user's guide
The symmetric eigenvalue problem
The symmetric eigenvalue problem
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Diffusive Load-Balancing Policies for Dynamic Applications
IEEE Concurrency
Lanczos Method: Evolution and Application
Lanczos Method: Evolution and Application
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
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
Parallel computation of the eigenvalues of symmetric Toeplitz matrices through iterative methods
Journal of Parallel and Distributed Computing
Fast eigenvalue calculations in a massively parallel plasma turbulence code
Parallel Computing
Implementation and tuning of a parallel symmetric Toeplitz eigensolver
Journal of Parallel and Distributed Computing
Strategies for spectrum slicing based on restarted Lanczos methods
Numerical Algorithms
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SIPs is a new efficient and robust software package implementing multiple shift-and-invert spectral transformations on parallel computers. Built on top of SLEPc and PETSc, it can compute very large numbers of eigenpairs for sparse symmetric generalized eigenvalue problems. The development of SIPs is motivated by applications in nanoscale materials modeling, in which the growing size of the matrices and the pathological eigenvalue distribution challenge the efficiency and robustness of the solver. In this article, we present a parallel eigenvalue algorithm based on distributed spectrum slicing. We describe the object-oriented design and implementation techniques in SIPs, and demonstrate its numerical performance on an advanced distributed computer.