A structure preserving Sort-Jacobi algorithm for computing eigenvalues or singular values is presented. The proposed method applies to an arbitrary semisimple Lie algebra on its (−1)-eigenspace of the Cartan involution. Local quadratic convergence for arbitrary cyclic schemes is shown for the regular case. The proposed method is independent of the representation of the underlying Lie algebra an...

We derive a formula for the backward error of a complex number λ when considered as an approximate eigenvalue of a Hermitian matrix pencil or polynomial with respect to Hermitian perturbations. The same are also obtained for approximate eigenvalues of matrix pencils and polynomials with related structures like skew-Hermitian, ∗-even and ∗-odd. Numerical experiments suggest that in many cases th...

Combating the effects of disorder on light transport in micro- and nano-integrated photonic devices is of major importance from both fundamental and applied viewpoints. In ordinary waveguides, imperfections and disorder cause unwanted back-reflections, which hinder large-scale optical integration. Topological photonic structures, a new class of optical systems inspired by quantum Hall effect an...

Non-Hermitian systems host unconventional physical effects that be used to design new optical devices. We study a non-Hermitian system consisting of 1D planar optical waveguides with suitable amount of simultaneous gain and loss. The parameter space contains an exceptional point, which can be accessed by varying the transverse gain and loss profile. When light propagates through the waveguide s...

We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kähler manifold X . These solutions are known to be related to polystable triples via a Kobayashi–Hitchin type correspondence. Using a characterization of infinitesimal deformations in terms of the cohomology of a certain elliptic double complex, we construct a Hermi...

of the Dissertation On geometric and motivic realizations of variations of Hodge structure over Hermitian symmetric domains

A Hermitian Einstein-Weyl manifold is a complex manifold admitting a Ricci-flat Kähler covering M̃ , with the deck transform acting on M̃ by homotheties. If compact, it admits a canonical Vaisman metric, due to Gauduchon. We show that a Hermitian Einstein-Weyl structure on a compact complex manifold is determined by its volume form. This result is a conformal analogue of Calabi’s theorem stating ...

We consider ergodic coherent MIMO channels. We characterize the optimal input distribution for various fading matrix distributions. First, we describe how symmetries in the fading matrix distribution are preserved as symmetries in the optimal input covariance and thus yield to specification of the optimal input. We will see that group structures and notion of commutant appear as key elements. S...

Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of x − λ, where λ is a unit element, are exhibited. When λ = 1, the generators of Euclidean and Hermitian dual codes of such codes are determined tog...

First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also determine minimal structured perturbations for which approximate eigenelements are exact eigenelements of the perturbed polynomials. Next, we analyze the effe...