20 papers · ranked by Valyu relevance
Benyamin Ghojogh, Fakhri Karray, Mark Crowley
This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also…
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.
Brendan Gavin, Agnieszka Międlar, Eric Polizzi
The linear FEAST algorithm is a method for solving linear eigenvalue problems. It uses complex contour integration to calculate the eigenvectors whose eigenvalues that are located inside some user-defined region in the complex plane. This makes it possible to parallelize the process of solving eigenvalue problems by…
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…
Mukhtar Karazym, Durvudkhan Suragan
Based on variational methods, we study a nonlinear eigenvalue problem for a quasilinear operator arising from smooth H¨ormander vector fields. We derive the smallest eigenvalue, prove its simplicity and isolatedness, establish the positivity of the first eigenfunction and show H¨older regularity of eigenfunctions.…
Henrik Eisenmann, Yuji Nakatsukasa
We present a new approach to compute selected eigenvalues and eigenvectors of the twoparameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter eigenvalue problem. The method is applicable for right definite problems…
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…
Fatima Aboud, François Jauberteau, Guy Moebs, Didier Robert
In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schr¨odinger pencils. Some recall are given for the pseudospectra. Then we present the numerical methods and results…
Bingjie Wu, Ramon Grima, Chen Jia
A survey of the literature reveals notable discrepancies among the purported exact results for the spectra of stochastic gene expression models. For self-repressing gene circuits, previous studies ([Phys. Rev. Lett. 99, 108103 (2007)], [Phys. Rev. E 83,062902 (2011)], [J. Chem. Phys. 160, 074105 (2024)], and [bioRxiv…
P. Cheema, M. M. Alamdari, G. A. Vio
Least Eigenvalue of an Unknown Mass Matrix Authors: ['P. Cheema' 'M. M. Alamdari' 'G. A. Vio'] In the field of structural engineering analysis, a common requirement is to calculate the modal frequencies of a structure that has undergone an update, either naturally (such as from material degradation), or due to manmade…
Authors not listed
A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…
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…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Sucheta Ghosh, Shankar Prasad Bhattacharyya
The quantum states of hydrogen atom in one dimension can be obtained by a careful application of the well-known Frobenius method. The exercise is highly educative and brings to focus the subtle aspects of quantum mechanics. The allowed states turn out to be only of odd parity and non-degenerate, having energy given by…
F. Robin O’Keefe, Julie A. Meachen, P. David Polly
This paper is concerned with rank deficiency in phenotypic covariance matrices: first to establish it is a problem by measuring it, and then proposing methods to treat for it. Significant rank deficiency can mislead current measures of whole-shape phenotypic integration, because they rely on eigenvalues of the…
Junya Watanabe
Quantification of the magnitude of trait covariation plays a pivotal role in the study of phenotypic evolution, for which statistics based on dispersion of eigenvalues of a covariance or correlation matrix—eigenvalue dispersion indices—are commonly used. This study remedies major issues over the use of these…
Calvin Guan, Ashis Gangopadhyay
Although there are many methods available in the literature to compare the covariance structures of two populations, few are suitable for clinical application due to the inability to account for covariate(s) that affect the dependence structure of the variables being investigated. A common method is to adjust the…
Authors not listed
This article is the second in a two-part tutorial review on electronic spin-dependent dynamics. In Part I, we presented the fundamental theory within the adiabatic Born– Huang framework that describes the interaction between nuclear motion and the elec- tronic (spin and spatial) degrees of freedom. In particular, we…