Related papers: A homotopy method for finding eigenvalues and eige…
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…
We consider linear spectral-meromorphic (s-meromorphic) OD operators at the real axis such that all local solutions to the eigenvalue problems are meromorphic for all $\lambda$. By definition, rank one algebro-geometrical operator $L$ admit…
It is known that every positive solution of a one-dimensional Gel'fand problem can be written explicitly. In this paper we obtain exact expressions of all the eigenvalues and eigenfunctions of the linearized eigenvalue problem at each…
We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…
Versions of GMRES with deflation of eigenvalues are applied to lattice QCD problems. Approximate eigenvectors corresponding to the smallest eigenvalues are generated at the same time that linear equations are solved. The eigenvectors…
Denton, Parke, Tao and Zhang gave a new method which determines eigenvectors from eigenvalues for Hermitian matrices with distinct eigenvalues. In this short note, we extend the above result to general Hermitian matrices.
We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix $A$. Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to…
By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in…
In this work, an exact solution to a new generalized nonlinear KdV partial differential equations has been investigated using homotopy analysis techniques. The mentioned partial differential equation has been solved using homotopy…
In this paper we study the rate of convergence of the eigenvalues of 1-dimensional rapidly oscillating $p-$laplacian type problems and find explicit order of convergence both in $k$ and in $\ve$. Moreover, explicit bounds on the constant…
We estimate the eigenvalues of connection Laplacians in terms of the non-triviality of the holonomy.
The Koopman operator is a powerful approach to global stability analysis of nonlinear systems, which provides a systematic procedure for Lyapunov function design. In this framework, Lyapunov functions are obtained through the eigenfunctions…
We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the…
We exhibit algorithms to compute systems of Hecke eigenvalues for spaces of Hilbert modular forms over a totally real field. We provide many explicit examples as well as applications to modularity and Galois representations.
We study the real and imaginary parts of the powers of the Volterra operator on $L^2[0,1]$, specifically their eigenvalues, their norms and their numerical ranges.
I propose a proof of the existence of the existence of eigenvectors and eigenvalues in the spirit of Argand's proof of the fundamental theorem of algebra. The proof only relies on Weierstrass's theorem, the definition of the inverse of a…
In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential…
Using our previously published algorithm, we analyze the eigenvectors of the generalized Laplacian for two metric graphs occurring in practical applications. As expected, localization of an eigenvector is rare and the network should be…
In this paper we study the interior transmission problem and transmission eigenvalues for multiplicative perturbations of linear partial differential operator of order $\ge 2$ with constant real coefficients. Under suitable growth…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…