14 papers · ranked by Valyu relevance
Alexandre Girouard, Antoine Henrot, Jean Lagacé
We study a new link between the Steklov and Neumann eigenvalues of domains in Euclidean space. This is obtained through an homogenisation limit of the Steklov problem on a periodically perforated domain, converging to a family of eigenvalue problems with dynamical boundary conditions. For this problem, the spectral…
Haoze He, Daniel Kressner, Bor Plestenjak
It is well known that a family of ${n}\times{n}$ commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the n joint eigenvalues of the family. In this work, we consider the task of numerically computing approximations to…
James S. Sims, María Bélen Ruiz
A computationally fast Fortran 90+ quadruple precision portable parallel GRSDEP (generalized real symmetric-definite eigenvalue problem) package suitable for large (80,000 x 80,000 or greater) dense matrices is discussed in this paper.
Alexander Pikovski, Dennis Salahub
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent variable. This method is applied to the numerical solution of the eigenvalue…
Thomas J. Anastasio, Andrea K. Barreiro, Jared C. Bronski
We consider the problem of finding the spectrum of an operator taking the form of a low-rank (rank one or two) non-normal perturbation of a well-understood operator, motivated by a number of problems of applied interest which take this form. We use the fact that the system is a low-rank perturbation of a solved…
Patrick Dumond, Natalie Baddour
An inverse eigenvalue problem approach to system design is considered. The Cayley-Hamilton theorem is developed for the general case involving the generalized eigenvalue vibration problem. Since many solutions exist for a desired frequency spectrum, a discussion of the required design information and suggestions for…
Marta M. Betcke, Heinrich Voss
In this work we present a new restart technique for iterative projection methods for nonlinear eigenvalue problems admitting minmax characterization of their eigenvalues. Our technique makes use of the minmax induced local enumeration of the eigenvalues in the inner iteration. In contrast to global numbering which…
Riccardo Alessandro, Ivan Giannì, Federica Pes, Tommaso Nottoli + 1 more
Equations Revisited: A Simple and Efficient Iterative Algorithm Authors: ['Riccardo Alessandro' 'Ivan Giannì' 'Federica Pes' 'Tommaso Nottoli' 'Filippo Lipparini'] We present an algorithm to solve the linear response equations for Hartree-Fock, Density Functional Theory, and the Multiconfigurational Self-Consistent…
Genjiao Zhou, Shoushi Wang, Jinhong Huang, Kathiravan Srinivasan
Tensor eigenproblems have wide applications in blind source separation, magnetic resonance imaging, and molecular conformation. In this study, we explore an alternating direction method for computing the largest or smallest Z-eigenvalue and corresponding eigenvector of an even-order symmetric tensor. The method…
Jia Zhao, Jieming Zhang
Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$J \in{\mathbb{R}}^{n\times n}$\end{document} J ∈ R n × n be a normal matrix such that…
Tuba Gulsen, Emrah Yilmaz, Sertac Goktas
We study the conformable fractional (CF) Dirac system with separated boundary conditions on an arbitrary time scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…
Daniel Kressner, Bor Plestenjak
The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the staircase form and then applying a standard solver, such as the QZ algorithm, to…
John W. Pearson, Jennifer Pestana, David J. Silvester
This paper is concerned with the implementation of efficient solution algorithms for elliptic problems with constraints. We establish theory which shows that including a simple scaling within well-established block diagonal preconditioners for Stokes problems can result in significantly faster convergence when applying…
Jianxing Zhao, Caili Sang
A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li et al. (Linear Algebra Appl. 481:36-53, [1]) and Huang et al. (J. Inequal. Appl. 2016:254, [2]). As an application of this set, new bounds for the minimum eigenvalue of \documentclass[12pt]{minimal}…