# Registered Data

Contents

- 1 [CT008]
- 1.1 [00770] Rellich eigendecomposition of paraHermitian matrices, with applications
- 1.2 [00430] Nearest singular pencil via Riemannian optimization
- 1.3 [02200] Structured Distances to Nearest Singular Matrix Pencil
- 1.4 [01156] Row completion of polynomial matrices
- 1.5 [00757] Effect of electrostatic forces and moments on cracked electrostrictive dielectrics

# [CT008]

**Session Time & Room****Classification**

## [00770] Rellich eigendecomposition of paraHermitian matrices, with applications

**Session Time & Room**:__1E__(Aug.21, 17:40-19:20) @__G304__**Type**: Contributed Talk**Abstract**: Let $H(z)$ be paraHermitian, that is, analytic and Hermitian on the unit circle $S^1$. We prove that $H(z)=U(z)D(z)U(z)^P$ where, for all $z \in S^1$, $U(z)$ is unitary, $U(z)^P=U(z)^*$, and $D(z)$ is real diagonal; moreover, $U(z), D(z)$ are analytic in $w=z^{1/N}$ for some positive integer $N$, and $U(z)^P$ is the paraHermitian conjugate of $U(z)$. We discuss the implications on the svd of an $S^1$-analytic matrix and the sign characteristics of unimodular eigenvalues of $*$-palindromic matrix polynomials.**Classification**:__15A23__,__15A18__,__15A54__,__15B57__**Format**: Talk at Waseda University**Author(s)**:**Vanni Noferini**(Aalto University)- Giovanni Barbarino (Aalto University)

## [00430] Nearest singular pencil via Riemannian optimization

**Session Time & Room**:__1E__(Aug.21, 17:40-19:20) @__G304__**Type**: Contributed Talk**Abstract**: The problem of finding the nearest complex $($real$)$ singular pencil can be cast as a minimization problem over the manifold $U(n) \times U(n)$ $\left( O(n) \times O(n) \right)$ via the generalized Schur form. This novel perspective yields a competitive numerical method by pairing it with an algorithm capable of doing optimization on a Riemannian manifold.**Classification**:__15A22__**Format**: Talk at Waseda University**Author(s)**:**Lauri Nyman**(Aalto University)

## [02200] Structured Distances to Nearest Singular Matrix Pencil

**Session Time & Room**:__1E__(Aug.21, 17:40-19:20) @__G304__**Type**: Contributed Talk**Abstract**: We consider the structured distance to singularity for a given regular matrix pencil $A+sE$, where $(A,E)\in \mathbb S \subseteq (\mathbb{C}^{n,n})^2$. This includes Hermitian, skew-Hermitian, $*$-even, $*$-odd, $*$-palindromic, T-palindromic, and dissipative Hamiltonian pencils. We derive explicit computable formulas for the distance to the nearest structured pencil $(A-\Delta_A)+s(E-\Delta_E)$ such that $A-\Delta_A$ and $E-\Delta_E$ have a common null vector. We then obtain a family of computable lower bounds for the unstructured and structured distances to singularity.**Classification**:__15A18__,__15A22__,__65K05__**Format**: Talk at Waseda University**Author(s)**:**Anshul Prajapati**(Indian Institute of Technology Delhi)- Punit Sharma (Indian Institute of Technology Delhi)

## [01156] Row completion of polynomial matrices

**Session Time & Room**:__1E__(Aug.21, 17:40-19:20) @__G304__**Type**: Contributed Talk**Abstract**: Perturbation problems arise frequently in applications, as in structural changes of the dynamics of a system or in pole placement problems in control theory. Perturbation problems of matrices are closely related to completion problems. We present a solution to the row-completion problem of a polynomial matrix, prescribing the eigenstructure of the resulting matrix and maintaining the degree.**Classification**:__15A22__,__15A83__**Author(s)**:- Agustzane Amparan (Universidad del País Vasco, UPV/EHU)
- Itziar Baragaña (Universidad del País Vasco, UPV/EHU)
- Silvia Marcaida (Universidad del País Vasco, UPV/EHU)
**Alicia Roca**(Universitat Politècnica de València )

## [00757] Effect of electrostatic forces and moments on cracked electrostrictive dielectrics

**Session Time & Room**:__1E__(Aug.21, 17:40-19:20) @__G304__**Type**: Contributed Talk**Abstract**: Going beyond the scope of solely mechanical considerations, fracture mechanics of smart dielectrics is additionally concerned with the implications of electric fields on crack tip loading. In this work, the oftentimes neglected electric body and surface forces as well as body couples stemming from the Maxwell stress tensor are studied in the context of a crack in an infinite electrostrictive dielectric by exploiting holomorphic potentials and Cauchy's integral formulae within the framework of complex analysis.**Classification**:__30E20__,__30E25__,__74A35__,__74R10__,__78A30__**Format**: Talk at Waseda University**Author(s)**:**Lennart Behlen**(University of Kassel)- Daniel Wallenta (University of Kassel)
- Andreas Ricoeur (University of Kassel)