Related papers: Solving singular generalized eigenvalue problems b…
The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of…
We describe algorithms for computing eigenpairs (eigenvalue--eigenvector) of a complex $n\times n$ matrix $A$. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not…
We study the complexity of solving the \emph{generalized MinRank problem}, i.e. computing the set of points where the evaluation of a polynomial matrix has rank at most $r$. A natural algebraic representation of this problem gives rise to a…
The multiparameter matrix pencil problem (MPP) is a generalization of the one-parameter MPP: given a set of $m\times n$ complex matrices $A_0,\ldots, A_r$, with $m\ge n+r-1$, it is required to find all complex scalars…
This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that…
This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial…
In applications of linear algebra including nuclear physics and structural dynamics, there is a need to deal with uncertainty in the matrices. We focus on matrices that depend on a set of parameters $\omega$ and we are interested in the…
This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high dimensional systems with tensor product structure when discretized with the stochastic Galerkin method.…
The inverse spectral problem for the second-order differential pencil with quadratic dependence on the spectral parameter is studied. We obtain sufficient conditions for the global solvability of the inverse problem, prove its local…
Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the…
We present SPEC-RE, a new algorithm to sort complex eigenvalues, generated as the solutions to algebraic equations, whose coefficients are analytic functions of one or many, possibly complex parameters. The fact that the eigenvalues are…
We study generalized eigenvalue problems for meet and join matrices with respect to incidence functions on semilattices. We provide new bounds for generalized eigenvalues of meet matrices with respect to join matrices under very general…
We solve the problem of characterizing the Kronecker structure of a matrix pencil obtained by a rank-one perturbation of another matrix pencil. The results hold over arbitrary fields.
We investigate a method to solve a class of Schr{\"o}dinger equation eigenvalue problems numerically to very high precision $P$ (from thousands to a million of decimals). The memory requirement, and the number of high precision algebraic…
A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by smoothing steps on a series of multilevel finite…
In this paper we are concerned to find the eigenvalues and eigenvectors of a real symetric matrix by applying a new numerical method similar to Jacobi method. Our approch consists to use a new orthogonal matrix. The computation of the…
We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…
We introduce an eigenvalue-preserving transformation algorithm from the generalized eigenvalue problem by matrix pencil of the upper and the lower bidiagonal matrices into a standard eigenvalue problem while preserving sparsity, using the…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…