A truncated-CG style method for symmetric generalized eigenvalue problems

Authors:
P. -A. Absil;C. G. Baker;K. A. Gallivan
Affiliations:
Department of Mathematical Engineering, Université catholique de Louvain, 1348 Louvain-la-Neuve, Belgium and Peterhouse, University of Cambridge, Cambridge CB2 1RD, UK;School of Computational Science, Florida State University, Tallahassee, FL 32306-4120, USA;School of Computational Science, Florida State University, Tallahassee, FL 32306-4120, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 15
Cited 5

The dynamics of Rayleigh quotient iteration

SIAM Journal on Numerical Analysis
An orthogonal accelerated deflation technique for large symmetric eigenproblems

Computer Methods in Applied Mechanics and Engineering
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems

SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
The symmetric eigenvalue problem

The symmetric eigenvalue problem
Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils

SIAM Journal on Scientific Computing
Templates for the solution of algebraic eigenvalue problems: a practical guide

Templates for the solution of algebraic eigenvalue problems: a practical guide
Trust-region methods

Trust-region methods
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
An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems

SIAM Journal on Scientific Computing
A Grassmann--Rayleigh Quotient Iteration for Computing Invariant Subspaces

SIAM Review
Convergence Analysis of Inexact Rayleigh Quotient Iteration

SIAM Journal on Matrix Analysis and Applications
Cubically Convergent Iterations for Invariant Subspace Computation

SIAM Journal on Matrix Analysis and Applications
Adaptive model trust region methods for generalized eigenvalue problems

ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I

Newton-KKT interior-point methods for indefinite quadratic programming

Computational Optimization and Applications
PRIMME: preconditioned iterative multimethod eigensolver—methods and software description

ACM Transactions on Mathematical Software (TOMS)
An implicit riemannian trust-region method for the symmetric generalized eigenproblem

ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
On optimizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere

Computational Optimization and Applications
A Rayleigh-Ritz style method for large-scale discriminant analysis

Pattern Recognition

Quantified Score

Hi-index	7.30

Visualization

Abstract

A numerical algorithm is proposed for computing an extreme eigenpair of a symmetric/positive-definite matrix pencil (A,B). The leftmost or the rightmost eigenvalue can be targeted. Knowledge of (A,B) is only required through a routine that performs matrix-vector products. The method has excellent global convergence properties and its local rate of convergence is superlinear. It is based on a constrained truncated-CG trust-region strategy to optimize the Rayleigh quotient, in the framework of a recently proposed trust-region scheme on Riemannian manifolds.