# MS-11 Matrix Polynomials

### Organizers: Froilán Dopico (Universidad Carlos III de Madrid, Spain) and Paul Van Dooren (Catholic University of Louvain, Belgium)

Matrix polynomials is a classical topic in Matrix Analysis that has received a lot of attention in the last decade. This renewed interest comes mainly from the necessity of improving the algorithms for computing the eigenvalues of Matrix Polynomials, both in terms of efficiency and accuracy, from the many applications where Matrix Polynomials arise, and from the key role that Matrix Polynomials play in solving more general nonlinear eigenvalue problems. As a consequence of these numerical and practical necessities many classical concepts in the theory of Matrix Polynomials have been revised, simplified, expanded, and set in more applied perspectives, as well as many new lines of theoretical research have been initiated and analyzed. This Mini-Symposium aims to give an overview of recent activity on Matrix Polynomials from the point of view of theory, applications, and numerical practice.

### Speakers

**Andrii Dmytryshyn**, LAA Early Career Speaker, *Generic matrix polynomials with fixed rank and fixed degree*

**María Isabel Bueno**, *A unified approach to Fiedler-like pencils via strong block minimal bases pencils.*

**Froilán Dopico**, *Paul Van Dooren's Index Sum Theorem and the solution of the inverse rational eigenvalue problem*

**Steve Mackey**, *Majorization and Matrix Polynomials*

**Silvia Marcaida**, *Extended spectral equivalence*

**Volker Mehrmann**, *Port-Hamiltonian Linearizations and Stability Radii for Systems Arising in Acoustic Field Computation*

**Javier Pérez**, *Structured backward error analyses of linearized polynomial eigenvalue problems*

**Leonardo Robol**, *Fast and backward stable computation of the eigenvalues of matrix polynomials*

**Philip Saltenberger**, *Block Kronecker Ansatz Spaces for Matrix Polynomials*

**Marc Van Barel**, *Solving polynomial eigenvalue problems by a scaled block companion linearization*

**Paul Van Dooren**, *Robustness and Perturbations of Minimal Bases*