%0 Journal Article %1 Mackey_2006 %A Mackey, D. Steven %A Mackey, Niloufer %A Mehl, Christian %A Mehrmann, Volker %D 2006 %I Society for Industrial & Applied Mathematics (SIAM) %J SIAM Journal on Matrix Analysis and Applications %K 15a18-eigenvalues-singular-values-and-eigenvectors 15b57-hermitian-skew-hermitian-and-related-matrices 65f15-numerical-eigenvalues-eigenvectors 93b60-controllability-observability-system-structure-eigenvalue-problems %N 4 %P 1029--1051 %R 10.1137/050628362 %T Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations %U https://epubs.siam.org/doi/10.1137/050628362 %V 28 %X Many applications give rise to nonlinear eigenvalue problems with an underlying structured matrix polynomial. In this paper several useful classes of structured polynomials (e.g., palindromic, even, odd) are identified and the relationships between them explored. A special class of linearizations which reflect the structure of these polynomials, and therefore preserve symmetries in their spectra, is introduced and investigated. We analyze the existence and uniqueness of such linearizations and show how they may be systematically constructed.

@article{Mackey_2006, abstract = {Many applications give rise to nonlinear eigenvalue problems with an underlying structured matrix polynomial. In this paper several useful classes of structured polynomials (e.g., palindromic, even, odd) are identified and the relationships between them explored. A special class of linearizations which reflect the structure of these polynomials, and therefore preserve symmetries in their spectra, is introduced and investigated. We analyze the existence and uniqueness of such linearizations and show how they may be systematically constructed.}, added-at = {2021-07-09T06:17:53.000+0200}, author = {Mackey, D. Steven and Mackey, Niloufer and Mehl, Christian and Mehrmann, Volker}, biburl = {https://www.bibsonomy.org/bibtex/29923e0a74a466d2bead7167ecc18aef7/gdmcbain}, doi = {10.1137/050628362}, interhash = {62042446ec0e7349bcea53b2c8acdee0}, intrahash = {9923e0a74a466d2bead7167ecc18aef7}, journal = {{SIAM} Journal on Matrix Analysis and Applications}, keywords = {15a18-eigenvalues-singular-values-and-eigenvectors 15b57-hermitian-skew-hermitian-and-related-matrices 65f15-numerical-eigenvalues-eigenvectors 93b60-controllability-observability-system-structure-eigenvalue-problems}, month = jan, number = 4, pages = {1029--1051}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, timestamp = {2021-07-09T06:18:34.000+0200}, title = {Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations}, url = {https://epubs.siam.org/doi/10.1137/050628362}, volume = 28, year = 2006 }