Related papers: Sensitivity and computation of a defective eigenva…
The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which…
In this paper, we discuss the sensitivity of quantum PageRank. By using the finite dimensional perturbation theory, we estimate the change of the quantum PageRank under a small analytical perturbation on the Google matrix. In addition, we…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
Quantum defects are atomic defects in materials that provide resources to construct quantum information devices such as single-photon emitters (SPEs) and spin qubits. Recently, two-dimensional (2D) materials gained prominence as a host of…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
In this paper, we discuss the ambiguous chance constrained based portfolio optimization problems, in which the perturbations associated with the input parameters are stochastic in nature, but their distributions are not known precisely. We…
We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…
The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
An adaptive algorithm for computing eigenmodes and propagation constants of optical fibers is proposed. The algorithm is built using a dual-weighted residual error estimator. The residuals are based on the eigensystem for leaky hybrid modes…
Contrary to an assumption made by Bojanczyk, Higham, and Patel [SIAM J. Matrix Anal. Appl., 24(4):914-931, 2003], a perturbation bound for indefinite least square problems is capable of arbitrarily large overestimates for all perturbations…
This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…
The standard approach for finding eigenvalues and eigenvectors of matrix polynomials starts by embedding the coefficients of the polynomial into a matrix pencil, known as linearization. Building on the pioneering work of Nakatsukasa and…
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…
The sensitivity of structural dynamic characteristics related to eigenmode (such as modal assurance criteria, modal flexibility, and modal mass etc.) has become a crucial and widely applied tool across various engineering fields. In this…
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…
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…
The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate…
We study the randomized $n$-th minimal errors (and hence the complexity) of vector valued approximation. In a recent paper by the author [Randomized complexity of parametric integration and the role of adaption I. Finite dimensional case…
The nonnegative inverse eigenvalue problem (NIEP) asks which lists of $n$ complex numbers (counting multiplicity) occur as the eigenvalues of some $n$-by-$n$ entry-wise nonnegative matrix. The NIEP has a long history and is a known hard…