An implicit riemannian trust-region method for the symmetric generalized eigenproblem

Authors:
C. G. Baker;P. -A. Absil;K. A. Gallivan
Affiliations:
School of Computational Science, Florida State University, Tallahassee, FL;Département d’ingénierie mathématique, Université catholique de Louvain, Louvain-la-Neuve, Belgium;School of Computational Science, Florida State University, Tallahassee, FL
Venue:
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Year:
2006

Citing 7
Cited 0

A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems

SIAM Journal on Matrix Analysis and Applications
The Geometry of Algorithms with Orthogonality Constraints

SIAM Journal on Matrix Analysis and Applications
The trace minimization method for the symmetric generalized eigenvalue problem

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Matrix algorithms

Matrix algorithms
Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method

SIAM Journal on Scientific Computing
Computing Eigenelements of Real Symmetric Matrices via Optimization

Computational Optimization and Applications
A truncated-CG style method for symmetric generalized eigenvalue problems

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

The recently proposed Riemannian Trust-Region method can be applied to the problem of computing extreme eigenpairs of a matrix pencil, with strong global convergence and local convergence properties. This paper addresses inherent inefficiencies of an explicit trust-region mechanism. We propose a new algorithm, the Implicit Riemannian Trust-Region method for extreme eigenpair computation, which seeks to overcome these inefficiencies while still retaining the favorable convergence properties.