Related papers: Structured conditioning of Hamiltonian eigenvalue …
The characteristic polynomial of the effective Hamiltonian for a general model has been discussed. It is found that, compared with the associated energy eigenvalues, this characteristic polynomial generally has better analytical properties…
In this paper, we consider the structured perturbation analysis for multiple right-hand side linear systems with parameterized coefficient matrix. Especially, we present the explicit expressions for structured condition numbers for multiple…
Combined perturbation bounds are presented for eigenvalues and eigenspaces of Hermitian matrices or singular values and singular subspaces of general matrices. The bounds are derived based on the smooth decompositions and elementary…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
We investigate the eigengenvalues problem for self-adjoint operators with the singular perturbations. The general results presented here includes weakly as well as strongly singular cases. We illustrate these results on two models which…
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…
We give a modified Hamiltonian for a particle in a box with infinite potential walls that takes into account wall effects. The Hamiltonian is expressed in both the position and momentum representation. In the momentum representation the…
The characterization of the solution set for a class of algebraic Riccati inequalities is studied. This class arises in the passivity analysis of linear time invariant control systems. Eigenvalue perturbation theory for the Hamiltonian…
The influence of multiplicative stochastic perturbations on the class of asymptotically Hamiltonian systems on the plane is investigated. It is assumed that disturbances do not preserve the equilibrium of the corresponding limiting system…
In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition…
We consider the sensitivity of real zeros of structured polynomial systems to perturbations of their coefficients. In particular, we provide explicit estimates for condition numbers of structured random real polynomial systems, and extend…
This paper is devoted to a structured perturbation analysis of the symmetric algebraic Riccati equations by exploiting the symmetry structure. Based on the analysis, the upper bounds for the structured normwise, mixed and componentwise…
We investigate singularly perturbed nonlinear complex differential systems of the form $\hbar \partial_x f = F (x, \hbar, f)$ where $\hbar$ is a small complex perturbation parameter. Under a geometric assumption on the eigenvalues of the…
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…
A standard perturbation result states that perturbed eigenvalues and eigenprojections admit a perturbation series provided that the operator norm of the perturbation is smaller than a constant times the corresponding eigenvalue isolation…
The condition number for eigenvalue computations is a well--studied quantity. But how small can we expect it to be? Namely, which is a perfectly conditioned matrix w.r.t. eigenvalue computations? In this note we answer this question with…
We present a discussion of the consequences in perturbation theory when an exact eigenfunctions and eigenvalues to to the zeroth order Hamiltonian $H_0$ cannot be found. Since the usual approximations such as projecting the wavefunction on…
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…
We consider the fractional powers of singular (point-like) perturbations of the Laplacian, and the singular perturbations of fractional powers of the Laplacian, and we compare such two constructions focusing on their perturbative structure…
The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or…