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[CT008]

CT008 (1/1) : Basic linear algebra (15A) / Miscellaneous topics of analysis in the complex plane (30E)

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)

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)

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)

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 )

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)