Related papers: Polynomial two-parameter eigenvalue problems and m…
A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need to be related back to matrix polynomials. In this paper we…
One of the main reasons for topological persistence being useful in data analysis is that it is backed up by a stability (isometry) property: persistence diagrams of $1$-parameter persistence modules are stable in the sense that the…
A delay Lyapunov matrix corresponding to an exponentially stable system of linear time-invariant delay differential equations can be characterized as the solution of a boundary value problem involving a matrix valued delay differential…
We propose subspace methods for 3-parameter eigenvalue problems. Such problems arise when separation of variables is applied to separable boundary value problems; a particular example is the Helmholtz equation in ellipsoidal and…
We consider a nonlinear non-autonomous system with time-varying delays $$ \dot{x_i}(t)=-a_i(t)x_{i}(h_i(t))+\sum_{j=1}^mF_{ij}(t,x_j(g_{ij}(t))) $$ which has a large number of applications in the theory of artificial neural networks. Via…
We consider the forward problem of uncertainty quantification for the generalised Dirichlet eigenvalue problem for a coercive second order partial differential operator with random coefficients, motivated by problems in structural…
In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two-field (displacement-pressure) and the three-field (stress-displacement-pressure) formulations. The method presented…
In this paper, we study a new type of stochastic functional differential equations which is called hybrid pantograph stochastic functional differential equations. We investigate several moment properties and sample properties of the…
We formulate a systematic elegant perturbative scheme for determining the eigenvalues of the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions when the normal derivative of {\psi} vanishes on an irregular closed…
Pencils of Hankel matrices whose elements have a joint Gaussian distribution with nonzero mean and not identical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which…
Many problems in physics, chemistry and other fields are perturbative in nature, i.e. differ only slightly from related problems with known solutions. Prominent among these is the eigenvalue perturbation problem, wherein one seeks the…
Kronecker coefficients encode the tensor products of complex irreducible representations of symmetric groups. Their stability properties have been considered recently by several authors (Vallejo, Pak and Panova, Stembridge). We describe a…
This paper investigates the eigenvalue computation problem of the dual quaternion Hermitian matrix closely related to multi-agent group control. Recently, power method was proposed by Cui and Qi in Journal of Scientific Computing, 100…
We study an interplay between delay and discontinuous hysteresis in dynamical systems. After having established existence and uniqueness of solutions, we focus on the analysis of stability of periodic solutions. The main object we study is…
Our goal is to study statistical properies of "dielectric resonances" which are poles of conductance of a large random $LC$ network. Such poles are a particular example of eigenvalues $\lambda_n$ of matrix pencils ${\bf H}-\lambda {\bf W}$,…
We revisit existence and stability of two-pulse solutions in the fifth-order Korteweg--de Vries (KdV) equation with two new results. First, we modify the Petviashvili method of successive iterations for numerical (spectral) approximations…
We propose a method for the treatment of two--point boundary value problems given by nonlinear ordinary differential equations. The approach leads to sequences of roots of Hankel determinants that converge rapidly towards the unknown…
It is known that a matrix polynomial with unitary matrix coefficients has its eigenvalues in the annular region $\frac{1}{2} < |\lambda| < 2$. We prove in this short note that under certain assumptions, matrix polynomials with either doubly…
We propose a new method for controlling linear dynamical systems under adversarial disturbances and cost functions. Our algorithm achieves a running time that scales polylogarithmically with the inverse of the stability margin, improving…
In Part I of this paper, we introduced a 2D eigenvalue problem (2DEVP) and presented theoretical results of the 2DEVP and its intrinsic connetion with the eigenvalue optimizations. In this part, we devise a Rayleigh quotient iteration…