Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Applied Mathematics
Instability Indices For Matrix Polynomials, Todd Kapitula, Elizabeth Hibma, Hwa Pyeong Kim, Jonathan Timkovich
Instability Indices For Matrix Polynomials, Todd Kapitula, Elizabeth Hibma, Hwa Pyeong Kim, Jonathan Timkovich
University Faculty Publications and Creative Works
There is a well-established instability index theory for linear and quadratic matrix polynomials for which the coefficient matrices are Hermitian and skew-Hermitian. This theory relates the number of negative directions for the matrix coefficients which are Hermitian to the total number of unstable eigenvalues for the polynomial. Herein we extend the theory to *-even matrix polynomials of any finite degree. In particular, unlike previously known cases we show that the instability index depends upon the size of the matrices when the degree of the polynomial is greater than two. We also consider Hermitian matrix polynomials, and derive an index which …
The Krein Matrix: General Theory And Concrete Applications In Atomic Bose-Einstein Condensates, Todd Kapitula, Panayotis G. Kevrekidis, Dong Yan
The Krein Matrix: General Theory And Concrete Applications In Atomic Bose-Einstein Condensates, Todd Kapitula, Panayotis G. Kevrekidis, Dong Yan
University Faculty Publications and Creative Works
When finding the nonzero eigenvalues for Hamiltonian eigenvalue problems it is especially important to locate not only the unstable eigenvalues (i.e., those with positive real part) but also those which are purely imaginary but have negative Krein signature. These latter eigenvalues have the property that they can become unstable upon collision with other purely imaginary eigenvalues; i.e., they are a necessary building block in the mechanism leading to the so-called Hamiltonian-Hopf bifurcation. In this paper we review a general theory for constructing a meromorphic matrix-valued function, the so-called Krein matrix, which has the property of not only locating the unstable …
The Krein Matrix: General Theory And Concrete Applications In Atomic Bose-Einstein Condensates, Todd Kapitula, Panayotis G. Kevrekidis, Dong Yan
The Krein Matrix: General Theory And Concrete Applications In Atomic Bose-Einstein Condensates, Todd Kapitula, Panayotis G. Kevrekidis, Dong Yan
University Faculty Publications and Creative Works
When finding the nonzero eigenvalues for Hamiltonian eigenvalue problems it is especially important to locate not only the unstable eigenvalues (i.e., those with positive real part) but also those which are purely imaginary but have negative Krein signature. These latter eigenvalues have the property that they can become unstable upon collision with other purely imaginary eigenvalues; i.e., they are a necessary building block in the mechanism leading to the so-called Hamiltonian-Hopf bifurcation. In this paper we review a general theory for constructing a meromorphic matrix-valued function, the so-called Krein matrix, which has the property of not only locating the unstable …