Paper Info
Title
Broyden's method for nonlinear eigenproblems.
Abstract
Broyden's method is a general method commonly used for nonlinear systems of equations when very little information is available about the problem. We develop an approach based on Broyden's method for the structure appearing in nonlinear eigenvalue problems. Our approach is designed for problems where the evaluation of a matrix vector product is computationally expensive, essentially as expensive as solving the corresponding linear system of equations. We show how the structure of the Jacobian matrix can be incorporated into the algorithm to improve convergence. The algorithm exhibits local superlinear convergence for simple eigenvalues, and we characterize the convergence. We show how deflation can be integrated and combined such that the method can be used to compute several eigenvalues. A specific problem in machine tool milling, coupled with a PDE, is used to illustrate the approach. The simulations were carried out using the Julia programming language, and the simulation software is provided publicly for reproducibility.
Year
DOI
Venue
2019
10.1137/18M1173150
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
nonlinear eigenproblems,Broyden methods,Newton methods,time-delay systems,eigenvalue problems
Convergence (routing),Applied mathematics,Mathematical optimization,Nonlinear system,Jacobian matrix and determinant,System of linear equations,Matrix vector product,Mathematics,Eigenvalues and eigenvectors,Machine tool,Broyden's method
Journal
Volume
Issue
ISSN
41
2
1064-8275
Citations 
PageRank 
References 
0
0.34
12
Authors
1
Name
Order
Citations
PageRank
Jarlebring Elias18411.48