Optimal quotients for solving large eigenvalue problems

Solving nonlinear eigenvalue problems

Solving Overdetermined Eigenvalue Problems

We propose a new interpretation of the generalized overdetermined eigenvalue problem (A− λB)v ≈ 0 for two m × n (m > n) matrices A and B, its stability analysis, and an efficient algorithm for solving it. Usually, the matrix pencil {A− λB} does not have any rank deficient member. Therefore we aim to compute λ for which A − λB is as close as possible to rank deficient; i.e., we search for λ that...

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