Related papers: Structured eigenvalue problems in electronic struc…
Dual quaternions and dual quaternion matrices have garnered widespread applications in robotic research, and its spectral theory has been extensively studied in recent years. This paper introduces the novel concept of the dual complex…
The eigenmodes of resonating structures, e.g., electromagnetic cavities, are sensitive to deformations of their shape. In order to compute the sensitivities of the eigenpair with respect to a scalar parameter, we state the Laplacian and…
The present paper introduces the analysis of the eigenvalue problem for the elasticity equations when the so called Navier-Lam\'e system is considered. Such a system introduces the displacement, rotation and pressure of some linear and…
Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries…
Over the last years, considerable attention has been paid to the role of the quaternion differential equations (QDEs) which extend the ordinary differential equations. The theory of QDEs was recently well established and it has wide…
Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to…
One can identify a tripartite classification of random matrix ensembles into geometrical universality classes corresponding to the plane, the sphere and the anti-sphere. The plane is identified with Ginibre-type (iid) matrices and the…
The algebraic Bethe Ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations.…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
The computation of electronic structure properties at the quantum level is a crucial aspect of modern physics research. However, conventional methods can be computationally demanding for larger, more complex systems. To address this issue,…
Let $A$ be a square matrix with a given structure (e.g. real matrix, sparsity pattern, Toeplitz structure, etc.) and assume that it is unstable, i.e. at least one of its eigenvalues lies in the complex right half-plane. The problem of…
We use ab initio electronic-structure methods to investigate random-matrix theory (RMT) universality in molecular electronic structure. Using single-reference electronic structure methods, including Hartree-Fock, configuration-interaction…
We investigate the statistical properties of eigenvalues of pseudo-Hermitian random matrices whose eigenvalues are real or complex conjugate. It is shown that when the spectrum splits into separated sets of real and complex conjugate…
The sensitivity of eigenvalues of structured matrices under general or structured perturbations of the matrix entries has been thoroughly studied in the literature. Error bounds are available and the pseudospectrum can be computed to gain…
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…
This book is about solving matrix nearness problems that are related to eigenvalues or singular values or pseudospectra. These problems arise in great diversity in various fields, be they related to dynamics, as in questions of robust…
Finding eigenvalue distributions for a number of sparse random matrix ensembles can be reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic mathematical theory of such equations exists, it has not been…
Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
Rotations and poses are ubiquitous throughout many fields of science and engineering such as robotics, aerospace, computer vision and graphics. In this paper, we provide a complete characterization of rotations and poses in terms of the…