Spectral decomposition of $(\star, ε)$-palindromic matrix polynomial and its applications
For researchers in matrix theory and control theory, this offers a theoretical framework for structured eigenvalue problems, but the results are incremental.
The paper provides a spectral decomposition of (★,ε)-palindromic quadratic matrix polynomials using a standard pair and parameter matrix, and applies it to solve inverse eigenvalue and eigenvalue embedding problems with no spill-over.
This paper provides the spectral decomposition of $(\star,ε)$-palindromic quadratic matrix polynomial $P(λ)$ by a standard pair and a parameter matrix. When $J$ is assumed to be a block diagonal matrix, the parameter matrix $Γ$ has a special structure. And then the spectral decomposition is applied to solve the inverse eigenvalue problem and the eigenvalue embedding problem with no spill-over.