Analysis of structured polynomial eigenvalue problems (original) (raw)

This thesis analyzes structured polynomial eigenvalue problems, focusing on Hermitian/symmetric, alternating, and palindromic matrix polynomials commonly used in applications like vibration analysis and optimal control. The work classifies quasidefinite Hermitian matrix polynomials and explores their eigenvalue distributions. Noteworthy approaches include generalized spectral decompositions, structured Jordan triples to address inverse polynomial eigenvalue problems, and the generation of new quadratic and cubic quasidefinite matrix polynomials from existing spectral data.