From Self-consistency to SOAR: Solving Large Scale NonlinearEigenvalue Problems

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What is common among electronic structure calculation, design of MEMS devices, vibrational analysis of high speed railways, and simulation of the electromagnetic field of a particle accelerator? The answer: they all require solving large scale nonlinear eigenvalue problems. In fact, these are just a handful of examples in which solving nonlinear eigenvalue problems accurately and efficiently is becoming increasingly important. Recognizing the importance of this class of problems, an invited minisymposium dedicated to nonlinear eigenvalue problems was held at the 2005 SIAM Annual Meeting. The purpose of the minisymposium was to bring together numerical analysts and application scientists to showcase ... continued below

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Bai, Zhaojun & Yang, Chao February 1, 2006.

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What is common among electronic structure calculation, design of MEMS devices, vibrational analysis of high speed railways, and simulation of the electromagnetic field of a particle accelerator? The answer: they all require solving large scale nonlinear eigenvalue problems. In fact, these are just a handful of examples in which solving nonlinear eigenvalue problems accurately and efficiently is becoming increasingly important. Recognizing the importance of this class of problems, an invited minisymposium dedicated to nonlinear eigenvalue problems was held at the 2005 SIAM Annual Meeting. The purpose of the minisymposium was to bring together numerical analysts and application scientists to showcase some of the cutting edge results from both communities and to discuss the challenges they are still facing. The minisymposium consisted of eight talks divided into two sessions. The first three talks focused on a type of nonlinear eigenvalue problem arising from electronic structure calculations. In this type of problem, the matrix Hamiltonian H depends, in a non-trivial way, on the set of eigenvectors X to be computed. The invariant subspace spanned by these eigenvectors also minimizes a total energy function that is highly nonlinear with respect to X on a manifold defined by a set of orthonormality constraints. In other applications, the nonlinearity of the matrix eigenvalue problem is restricted to the dependency of the matrix on the eigenvalues to be computed. These problems are often called polynomial or rational eigenvalue problems In the second session, Christian Mehl from Technical University of Berlin described numerical techniques for solving a special type of polynomial eigenvalue problem arising from vibration analysis of rail tracks excited by high-speed trains.

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  • Journal Name: SIAM News; Journal Volume: 39; Journal Issue: 3; Related Information: Journal Publication Date: April, 2006

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  • Report No.: LBNL--60645
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 901040
  • Archival Resource Key: ark:/67531/metadc882204

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  • February 1, 2006

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  • Sept. 22, 2016, 2:13 a.m.

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  • Sept. 22, 2017, 3:07 p.m.

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Bai, Zhaojun & Yang, Chao. From Self-consistency to SOAR: Solving Large Scale NonlinearEigenvalue Problems, article, February 1, 2006; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc882204/: accessed November 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.