Article
Tridiagonal Matrices and Boundary Conditions
SIAM Journal of Matrix Analysis and Applications
Document Type
Article
Publication Date
1-1-2016
Subjects
- Eigenvalues,
- Boundary Conditions (Differential Equations),
- Matrices
Disciplines
Abstract
We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end of a one-dimensional flock. We apply our results to demonstrate how asymptotic stability for consensus and flocking systems depends on the imposed boundary condition.
DOI
10.1137/140978909
Persistent Identifier
http://archives.pdx.edu/ds/psu/17473
Citation Information
Veerman, J. J. P., & Hammond, D. K. (2016). Tridiagonal Matrices and Boundary Conditions. SIAM Journal on Matrix Analysis and Applications, 37(1), 1-17.
This is the publisher's final PDF. Copyright (2016) Society for Industrial and Applied Mathematics. This is an open access article distributed under the Creative Commons Attribution License: https://creativecommons.org/licenses/by-nc-nd/4.0/
Version of record can be found at http://dx.doi.org/10.1137/140978909