Related papers: On Some Inverse Eigenvalue Problems of Quadratic P…
I revisit the so called "bispectral problem" introduced in a joint paper with Hans Duistermaat a long time ago, allowing now for the differential operators to have matrix coefficients and for the eigenfunctions, and one of the eigenvalues,…
A quasi-Toeplitz (QT) matrix is a semi-infinite matrix of the form $A=T(a)+E$ where $T(a)$ is the Toeplitz matrix with entries $(T(a))_{i,j}=a_{j-i}$, for $a_{j-i}\in\mathbb C$, $i,j\ge 1$, while $E$ is a matrix representing a compact…
We investigate the $t$-$W$ scheme for the anti-ferromagnetic XXX spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of transfer matrix. Based on it, we obtain the exact solution…
Let $K$ be a totally real field and $\pi$ be a regular algebraic polarized cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb A_K)$. Let $\{\rho_{\pi,\lambda}:\mathrm{Gal}_K\to\mathrm{GL}_n(\overline E_\lambda)\}_\lambda$ be the…
Given a quantum semitoric system composed of pseudodifferential operators, Berezin-Toeplitz operators, or a combination of both, we obtain explicit formulas for recovering, from the semiclassical asymptotics of the joint spectrum, all…
The eigenstates of a diagonalizable PT-symmetric Hamiltonian satisfy unconventional completeness and orthonormality relations. These relations reflect the properties of a pair of bi-orthonormal bases associated with non-hermitean…
The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…
Pole-swapping algorithms, generalizations of bulge-chasing algorithms, have been shown to be a viable alternative to the bulge-chasing QZ algorithm for solving the generalized eigenvalue problem for a matrix pencil A - {\lambda}B. It is…
This paper presents an innovative set of tools developed to support a methodology to find the left eigenvalues of $m$ order quaternion square matrix. It is solving four real polynomial equations of order not greater than $4m-3$ in four…
We consider a quadrature-based eigensolver to find eigenpairs of Hermitian matrices arising in lattice quantum chromodynamics. To reduce the computational cost for finding eigenpairs of such Hermitian matrices, we propose a new technique…
Inverse spectral problem for a self-adjoint differential operator, which is the sum of the operator of the third derivative on a finite interval and of the operator of multiplication by a real function (potential), is solved. Closed system…
We consider a periodic-parabolic eigenvalue problem with a non-negative potential $\lambda m$ vanishing on a non-cylindrical domain $D_m$ satisfying conditions similar to those for the parabolic maximum principle. We show that the limit as…
The spectral transformation Lanczos method for the sparse symmetric definite generalized eigenvalue problem for matrices $A$ and $B$ is an iterative method that addresses the case of semidefinite or ill conditioned $B$ using a shifted and…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
We consider the inverse problem of determining the highly oscillatory coefficient $a^\epsilon$ in partial differential equations of the form $-\nabla\cdot (a^\epsilon\nabla u^\epsilon)+bu^\epsilon = f$ from given measurements of the…
The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D…
We consider the class of bounded symmetric Jacobi matrices $J$ with positive off-diagonal elements and complex diagonal elements. With each matrix $J$ from this class, we associate the spectral data, which consists of a pair $(\nu,\psi)$.…
In present article the self-contained derivation of eigenvalue inverse problem results is given by using a discrete approximation of the Schroedinger operator on a bounded interval as a finite three-diagonal symmetric Jacobi matrix. This…
Quadratic permutation polynomial interleavers over integer rings have recently received attention in practical turbo coding systems from deep space applications to mobile communications. In this correspondence, a necessary and sufficient…
It is shown that the problem of balancing a nonnegative matrix by positive diagonal matrices can be recast as a constrained nonlinear multiparameter eigenvalue problem. Based on this equivalent formulation some adaptations of the power…