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Search · four archives
21 papers · ranked by Valyu relevance
Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak
Generalized eigenvalue problems involving a singular pencil are very challenging to solve, both with respect to accuracy and efficiency. The existing package Guptri is very elegant but may be time-demanding, even for small and medium-sized matrices. We propose a simple method to compute the eigenvalues of singular…
Karl Meerbergen, Zhijun Wang
The numerical solution of singular generalized eigenvalue problems is still challenging. In Hochstenbach, Mehl, and Plestenjak, Solving Singular Generalized Eigenvalue Problems by a Rank-Completing Perturbation, SIMAX 2019, a rank-completing perturbation was proposed and a related bordering of the singular pencil. For…
Tomaž Košir, Bor Plestenjak
In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems, which is a key relation for many theoretical results and numerical methods for…
Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak
problems Authors: ['Michiel E. Hochstenbach' 'Christian Mehl' 'Bor Plestenjak'] Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were developed. We show that all three approaches can be…
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…
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…
Yannis Voet, Espen Sande, Annalisa Buffa
Mass scaling is widely used in finite element models of structural dynamics for increasing the critical time step of explicit time integration methods. While the field has been flourishing over the years, it still lacks a strong theoretical basis and mostly relies on numerical experiments as the only means of…
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…
Jinzhi Huang, Zhongxiao Jia
For the computation of the generalized singular value decomposition (GSVD) of a large matrix pair (A,B) of full column rank, the GSVD is commonly formulated as two mathematically equivalent generalized eigenvalue problems, so that a generalized eigensolver can be applied to one of them and the desired GSVD components…
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…
Mohamed Jleli, Bessem Samet
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,q)$\end{document} ( p , q ) -Laplacian systems Authors: ['Mohamed Jleli' 'Bessem Samet'] We establish Lyapunov-type…
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…
Sri Priya Ponnapalli, Michael A. Saunders, Charles F. Van Loan, Orly Alter + 1 more
'Orly Alter' 'Dongxiao Zhu'] The number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing in many areas of science, accompanied by a need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. The only such framework to date…
Yan Hong, Dongkyu Lim, Feng Qi
In the paper, the authors establish some inequalities for generalized eigenvalues of perturbation problems on Hermitian matrices and modify shortcomings of some known inequalities for generalized eigenvalues in the related literature.
Tracey Oellerich, Maria Emelianenko, Lance Liotta, Robyn P. Araujo
This work is focused on Ordinary Differential Equations(ODE)-based models of biochemical systems that possess a singular Jacobian manifesting in non-hyperbolic equilibria. We show that there are several classes of systems that exhibit this behavior: a)systems with monomial-type interaction terms and b)systems with…
Iqbal M. Batiha, Reyad El-Khazali, Ahmed AlSaedi, Shaher Momani
This paper introduces a general solution of singular fractional-order linear-time invariant (FoLTI) continuous systems using the Adomian Decomposition Method (ADM) based on the Caputo's definition of the fractional-order derivative. The complexity of their entropy lies in defining the complete solution of such systems…
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…
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…
Authors not listed
Molecular polaritons are hybrid states formed by the quantum mechanical interaction between light and matter. Recent experiments have shown the ability to drastically modify chemical reactions in both the ground and excited states through the hybridization of the electronic and photonic degrees of freedom. Ab initio…
Derek Beaton, Kelly M. Sunderland, Brian Levine, Jennifer Mandzia + 6 more
The minimum covariance determinant (MCD) algorithm is one of the most common techniques to detect anomalous or outlying observations. The MCD algorithm depends on two features of multivariate data: the determinant of a matrix (i.e., geometric mean of the eigenvalues) and Mahalanobis distances (MD). While the MCD…
Feng Liu, Jay Rosenberger, Jing Qin, Yifei Lou + 1 more
To infer brain source activation patterns under different cognitive tasks is an integral step to understand how our brain works. Traditional electroencephalogram (EEG) Source Imaging (ESI) methods usually do not distinguish task-related and spurious non-task-related sources that jointly generate EEG signals, which…