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Eigenvalue and Generalized Eigenvalue Problems: Tutorial [PDF]

arXiv, 2019
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 provide examples from machine learning,
Ghojogh, Benyamin, Karray, Fakhri, Crowley, Mark   +2 more
arxiv   +3 more sources

Synchronizability of Multi-Layer Dual-Center Coupled Star Networks

Frontiers in Physics, 2021
In the research on complex networks, synchronizability is a significant measurement of network nature. Several research studies center around the synchronizability of single-layer complex networks and few studies on the synchronizability of multi-layer ...
Jian Zhu, Jian Zhu, Da Huang, Zhiyong Yu, Ping Pei   +4 more
doaj   +1 more source

Estimation of eigenvalues for the α-Laplace operator on pseudo-slant submanifolds of generalized Sasakian space forms

AIMS Mathematics, 2022
In this study, we seek to establish new upper bounds for the mean curvature and constant sectional curvature of the first positive eigenvalue of the α-Laplacian operator on Riemannian manifolds.
Meraj Ali Khan, Ali H. Alkhaldi , Mohd. Aquib   +2 more
doaj   +1 more source

Generalized eigenvalue problems with specified eigenvalues [PDF]

IMA Journal of Numerical Analysis, 2013
We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness for two applications.
D. Kressner, E. Mengi, I. Naki , N. Truhar   +3 more
openaire   +7 more sources

Nonlinear Eigenvalue Problems with Specified Eigenvalues [PDF]

SIAM Journal on Matrix Analysis and Applications, 2014
This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem $T$, we are concerned with finding the minimal backward error such that $T$ has a set of prescribed eigenvalues with prescribed algebraic multiplicities.
Michael Karow, Daniel Kressner, Emre Mengi   +2 more
openaire   +7 more sources

Fusing Eigenvalues [PDF]

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019
In this paper, we propose a new regularized (penalized) co-variance matrix estimator which encourages grouping of the eigenvalues by penalizing large differences (gaps) between successive eigenvalues. This is referred to as fusing eigenval-ues (eFusion), The proposed penalty function utilizes Tukey's biweight function that is widely used in robust ...
Ollila, Esa, Drašković, G., Pascal, F., Basiri, Shahab   +4 more
openaire   +5 more sources

Count of eigenvalues in the generalized eigenvalue problem [PDF]

Journal of Mathematical Physics, 2010
We study isolated and embedded eigenvalues in the generalized eigenvalue problem defined by two self-adjoint operators with a positive essential spectrum and a finite number of isolated eigenvalues. The generalized eigenvalue problem determines the spectral stability of nonlinear waves in infinite-dimensional Hamiltonian systems. The theory is based on
Marina Chugunova, Dmitry E. Pelinovsky
openaire   +3 more sources

Investigation of spectrum curves for a Sturm-Liouville problem with two-point nonlocal boundary conditions

Mathematical Modelling and Analysis, 2020
The article investigates the Sturm–Liouville problem with one classical and another nonlocal two-point boundary condition. We analyze zeroes, poles and critical points of the characteristic function and how the properties of this function depend on ...
Kristina Bingelė, Agnė Bankauskienė, Artūras Štikonas   +2 more
doaj   +1 more source

Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order

Advances in Nonlinear Analysis, 2022
In this paper, we investigate the buckling problem of the drifting Laplacian of arbitrary order on a bounded connected domain in complete smooth metric measure spaces (SMMSs) supporting a special function, and successfully obtain a general inequality for
Du Feng, Hou Lanbao, Mao Jing, Wu Chuanxi   +3 more
doaj   +1 more source

Transmission eigenvalues [PDF]

Inverse Problems, 2013
In inverse scattering theory, transmission eigenvalues can be seen as the extension of the notion of resonant frequencies for impenetrable objects to the case of penetrable dielectrics. The transmission eigenvalue problem is a relatively late arrival to the spectral theory of partial differential equations.
Cakoni, Fioralba, Haddar, Houssem
openaire   +8 more sources