Adaptive model trust region methods for generalized eigenvalue problems

Authors:
P. -A. Absil;C. G. Baker;K. A. Gallivan;A. Sameh
Affiliations:
School of Computational Science, Florida State University, Tallahassee, FL;School of Computational Science, Florida State University, Tallahassee, FL;School of Computational Science, Florida State University, Tallahassee, FL;Department of Computer Sciences, Purdue University, West Lafayette, IN
Venue:
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Year:
2005

Citing 6
Cited 1

The symmetric eigenvalue problem

The symmetric eigenvalue problem
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
Adaptive Eigenvalue Computations Using Newton's Method on the Grassmann Manifold

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

SIAM Journal on Matrix Analysis and Applications

A truncated-CG style method for symmetric generalized eigenvalue problems

Journal of Computational and Applied Mathematics

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Abstract

Computing a few eigenpairs of large-scale matrices is a significant problem in science and engineering applications and a very active area of research. In this paper, two methods that compute extreme eigenpairs of positive-definite matrix pencils are combined into a hybrid scheme that inherits the advantages of both constituents. The hybrid algorithm is developed and analyzed in the framework of model-based methods for trace minimization.