Wednesday, July 16

10:30 AM-12:30 PM
Building 200, Room 2

Preconditioned Methods for Large Eigenproblems

Large eigenvalue problems are of major importance in many grand challenge scientific and engineering applications: structural dynamics and buckling, ocean modeling, quantum chemistry, and magnetohydrodynamics. They arise typically from the discretization of continuous models, described by systems of partial differential equations. Matrices may be so large that the standard numerical methods become unsatisfactory and cannot be implemented even on the most powerful modern supercomputers as they are too slow or require too much memory.

Preconditioned iterative methods were specially designed for problems of that kind and now they are well understood for solving large ill-conditioned linear algebraic systems of equations. For eigenproblems the theory is still poor, and these methods are rarely used. Ideally, the methods would compute well-separated clusters of eigenvalues and corresponding eigenspaces at the same order of computational cost as that for solution of the corresponding linear algebraic system.

The purpose of the minisymposium is to bring together researchers in the area to discuss recent developments. Intended audience includes specialists in numerical linear algebra as well as researchers interested in applications.

Organizer: Andrew V. Knyazev
University of Colorado, Denver

10:30 Formulations of Preconditioning Techniques for Eigenvalue Problems
Yousef Saad, Andreas Stathopoulos, and Kesheng Wu, University of Minnesota, Minneapolis
(Cancelled)11:00 A Block Arnoldi-Faber Method for Large Complex Non Hermitian Eigenvalue Problems
Miloud Sadkane and Vincent Heuveline, IRISA-INRIA, France
11:30 Classical and Composite Orthogonal Projection Methods for Large Eigenproblems
Zhongxiao Jia, Dalian University of Technology, People's Republic of China
12:00 Forty Years of Preconditioned Iterative Methods for Large Symmetric Eigenvalue Problems
Andrew V. Knyazev, Organizer

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MMD, 3/31/97
tjf, 5/29/97
MMD, 7/3/97