2005 SIAM Annual Meeting
MS 44 and MS56: Nonlinear Eigenvalue Problems

Objective

Nonlinear eigenvalue problems (NEP) arise in a variety of scientific applications. These problems are considerably more difficult tto solve than the standard linear eigenvalue problems. Even for the simplest type of NEP, i.e., quadratic eigenvalue problems, which often encounters in structure dynamic analysis, seeking a solution that preserves certain structure of the underlying physical system may prove to be chanllenging. For general nonlinear eigenvalue problems arising from quantum chemistry, the convergence of the existing algorithm is still poorly understood. The sheer size of these problems requires us to seek more efficient and scalable apporaches. The purpose of this minisymposium is to discuss the latest algorithmic development of numerical solution to NEPs and to examine the effectiveness of these developments in real applications.

Organizers

• Zhaojun Bai, University of California, Davis
• Chao Yang, Lawrence Berkeley National Laboratory

Presentations (Speakers)

• Solving nonlinear eigenvalue problems in electronic structure calculations
  Chao Yang, Juan Meza and Lin-wang Wang, Lawrence Berkeley National Lab.

• Multiresolution solution of nonlinear intergral eigen-problems in electronic structure
  George I. Fann, Zhengting Gan, Robert J. Harrison, Oak Ridge National Lab., University of Tennessee, Knoxville, and Gregory Beylkin, University of Colorado

• Iterative projection methods for general nonlinear eigenproblems
  Heinrich Voss, Hamburg University of Technology, Germany

• Eigenproblem in Resonant MEMS Design
  David Bindel, University of California, Berkeley

• Reduction of nonlinear eigenproblems with JD
  Henk van der Vorst, Utrecht University

• A structure-preserving method for large scale eigenproblems of skew-Hamiltonian/Hamiltonian (SHH) pencils
  Yangfeng Su, Fudan University and Zhaojun Bai, University of California, Davis

• On a nonlinear eigenvalue problems arising in the vibration analysis of high speed trains
  Christian Mehl, Andreas Hilliges and Volker Mehrmann, Technical University Berlin.

• Solving nonlinear eigenproblems in accelerator cavity design
  Lie-Quan Lee, L. Ge, Z. Li, C. Ng and K. Ko, Stanford Linear Accelerator Center, and B. Liao, Z. Bai, University of California, Davis and W. Gao, C. Yang, P. Husbands and E. G. Ng, Lawrence Berkeley National Lab.

SIAM News Article

• From Self-Consistency to SOAR: Solving Large-Scale Nonlinear Eigenvalue Problems, SIAM News, Vol. 39, No. 3, April 2006 pdf file