Related papers: Structural backward stability in rational eigenval…
Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of…
Solitons are typically stable objects in 1D models, but their straightforward extensions to 2D and 3D settings tend to be unstable. In particular, the ubiquitous nonlinear Schroedinger (NLS) equation with the cubic self-focusing, creates…
We perform accurate investigation of stability of localized vortices in an effectively two-dimensional ("pancake-shaped") trapped BEC with negative scattering length. The analysis combines computation of the stability eigenvalues and direct…
We consider increasing stability in the inverse Schr\"{o}dinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are…
We study the stability of the Lanczos algorithm run on problems whose eigenvector empirical spectral distribution is near to a reference measure with well-behaved orthogonal polynomials. We give a backwards stability result which can be…
We investigate the problem of checking if a finite-state transducer is robust to uncertainty in its input. Our notion of robustness is based on the analytic notion of Lipschitz continuity --- a transducer is K-(Lipschitz) robust if the…
We introduce a backward stable algorithm for computing the CS decomposition of a partitioned $2n \times n$ matrix with orthonormal columns, or a rank-deficient partial isometry. The algorithm computes two $n \times n$ polar decompositions…
We consider the problem to reconstruct a wave speed $c \in C^\infty(M)$ in a domain $M \subset \R^n$ from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map $\Lambda$. We introduce a reconstruction formula…
We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalization of matrices of dimension N…
This paper is concerned with the extraction of the smallest eigenvalue and the corresponding eigenvector of a symmetric positive definite matrix pencil. We reveal implicit convexity of the eigenvalue problem in Euclidean space. A provable…
Given a real-valued positive semidefinite matrix, Williamson proved that it can be diagonalised using symplectic matrices. The corresponding diagonal values are known as the symplectic spectrum. This paper is concerned with the stability of…
Generalized eigenvalue problems involving a singular pencil are very challenging to solve, both with respect to accuracy and efficiency. The existing package Guptri is very elegant but may sometimes be time-demanding, even for small and…
A comprehensive, temporal and spatiotemporal linear stability analyses of a (driven) Oldroyd-B fluid with Poiseuille base flow profile in a horizontally aligned, square, Hele-Shaw cell is reported to identify the viable regions of…
In the present work, we consider the self-focusing discrete nonlinear Schrodinger equation on hexagonal and honeycomb lattice geometries. Our emphasis is on the study of the effects of anisotropy, motivated by the tunability afforded in…
The main objective of this talk is to develop a matrix pencil approach for the study of an initial value problem of a class of singular linear matrix differential equations whose coefficients are constant matrices. By using matrix pencil…
Results concerning the existence and spectral stability and instability of multiple periodic wave solutions for the nonlinear Schr\"odinger system with \textit{dnoidal} and \textit{cnoidal} profile will be determined in this manuscript. The…
The spectral decomposition of regular sl_2-invariant R-matrices R(lambda) is studied by means of the method of reduction of the Yang-Baxter equation onto subspaces of a given spin. Restrictions on the possible structure of several highest…
In this paper we give a closed formula for the graded dimension of the cyclotomic quiver Hecke algebra $R^\Lambda(\beta)$ associated to an {\it arbitrary} symmetrizable Cartan matrix $A=(a_{ij})_{i,j}\in I$, where $\Lambda\in P^+$ and…
In this paper, we develop new theory connected with resonant vector bundles that will allow for the use of validated numerics to rigorously determine the stability of pulse solutions in the context of the Swift-Hohenberg equation. For many…
Williamson's theorem states that for any $2n \times 2n$ real positive definite matrix $A$, there exists a $2n \times 2n$ real symplectic matrix $S$ such that $S^TAS=D \oplus D$, where $D$ is an $n\times n$ diagonal matrix with positive…