Solving generalized eigenvalue problems for large scale fluid-structure computational models with mid-power computers

Solving Large-scale Quadratic Eigenvalue Problems with Hamiltonian Eigenstructure Using a Structure-preserving Krylov Subspace Method

We consider the numerical solution of quadratic eigenproblems with spectra that exhibit Hamiltonian symmetry. We propose to solve such problems by applying a Krylov-Schur-type method based on the symplectic Lanczos process to a structured linearization of the quadratic matrix polynomial. In order to compute interior eigenvalues, we discuss several shift-and-invert operators with Hamiltonian str...

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...

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 ...

Lecture Notes on Solving Large Scale Eigenvalue Problems

A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.