Cracking large-scale eigenvalue problems, part II: Implementations

Large - Scale Eigenvalue Problems in Structural Dynamics

Parallel Evolutionary Computation in Very Large Scale Eigenvalue Problems

The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions [21]. This paper reports on new methods for finding eigenvalues of very large matrices by a synthesis of evolutionary computation, parallel programming, and e...

Solving Large-Scale Eigenvalue Problems on Vector Parallel Processors

We consider the development and implementation of eigen-solvers on distributed memory parallel arrays of vector processors and show that the concomitant requirements for vectorization and paralleliza-tion lead both to novel algorithms and novel implementation techniques. Performance results are given for several large-scale applications and some performance comparisons made with LAPACK and ScaL...

Iterative Projection Methods for Large–scale Nonlinear Eigenvalue Problems

In this presentation we review iterative projection methods for sparse nonlinear eigenvalue problems which have proven to be very efficient. Here the eigenvalue problem is projected to a subspace V of small dimension which yields approximate eigenpairs. If an error tolerance is not met then the search space V is expanded in an iterative way with the aim that some of the eigenvalues of the reduc...

Solving Large-scale Eigenvalue Problems in SciDAC Applications

Large-scale eigenvalue problems arise in a number of DOE applications. This paper provides an ovcrvicw of thc recent dcvclopriicrit of cigciivaluc computation in the coritcxt of two SciDAC applications. We emphasize the importance of Krylov suhspace methods, and point out its limitations. M7e discuss the value of alternative approaches that are more amenable to the use of prcconditioncrs, arid ...