Related papers: Conditioning and backward errors for nonlinear eig…
We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For…
The correlation spectrum of fully developed one-dimensional mappings are studied near and at a weakly intermittent situation. Using a suitable infinite matrix representation, the eigenvalue equation of the Frobenius-Perron operator is…
We perform a smoothed analysis of the componentwise condition numbers for determinant computation, matrix inversion, and linear equations solving for sparse n times n matrices. The bounds we obtain for the ex- pectations of the logarithm of…
Nonlinear eigenvalue equations arise naturally in quantum information theory, particularly in the variational quantification of entanglement. In this work, we present a hybrid analytical and numerical framework for evaluating the geometric…
The main of this work is to use the unit lower triangular matrices for solving inverse eigenvalue problem of nonnegative matrices and present the easier method to solve this problem.
We address the problem of computing the eigenvalue backward error of the Rosenbrock system matrix under various types of block perturbations. We establish computable formulas for these backward errors using a class of minimization problems…
We propose an iterative method to find pointwise growth exponential growth rates in linear problems posed on essentially one-dimensional domains. Such pointwise growth rates capture pointwise stability and instability in extended systems…
An new eigenvalue $\mathbb R$-linear problem arisen in the theory of metamaterials is stated and constructively investigated for circular non-overlapping inclusions. An asymptotic formula for eigenvalues is deduced when the radii of…
We derive new perturbation bounds for eigenvalues of Hermitian matrices with block structures. The structures we consider range from a standard 2-by-2 block form to block tridiagonal and tridigaonal forms. The main idea is the observation…
In this paper, we employed linear algebra and functional analysis to determine necessary and sufficient conditions for oscillation-free and stable solutions to linear and nonlinear parabolic partial differential equations. We applied…
One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…
We consider the nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. Using composition operators on Sobolev spaces, we establish embeddings of Sobolev spaces into weighted Lebesgue spaces. These…
This paper concerns some inverse eigenvalue problems of the quadratic $\star$-(anti)-palindromic system $Q(\lambda)=\lambda^2 A_1^{\star}+\lambda A_0 + \epsilon A_1$, where $\epsilon=\pm 1$, $A_1, A_0 \in \mathbb{C}^{n\times n}$,…
We consider real non-symmetric matrices and their factorisation as a product of real symmetric matrices. The number of complex eigenvalues of the original matrix reveals restrictions on such factorisations as we shall prove.
We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…
We study the eigenvalues and eigenfunctions of a differential operator that governs the asymptotic behavior of the unsupervised learning algorithm known as Locally Linear Embedding when a large data set is sampled from an interval or disc.…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…
We investigate the relation between the spectrum of a non-normal matrix and the norm of its resolvent. We provide spectral estimates for the resolvent of matrices whose largest singular value is bounded by $1$ (so-called Hilbert space…
We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form $T(\lambda)v=0$ that admit a variational characterization of eigenvalues. These problems arise in a variety of applications and are…