Search results for "Divide-and-conquer eigenvalue algorithm"
showing 6 items of 6 documents
Inverse eigenvalue problem for normal J-hamiltonian matrices
2015
[EN] A complex square matrix A is called J-hamiltonian if AT is hermitian where J is a normal real matrix such that J(2) = -I-n. In this paper we solve the problem of finding J-hamiltonian normal solutions for the inverse eigenvalue problem. (C) 2015 Elsevier Ltd. All rights reserved.
The inverse eigenvalue problem for a Hermitian reflexive matrix and the optimization problem
2016
The inverse eigenvalue problem and the associated optimal approximation problem for Hermitian reflexive matrices with respect to a normal {k+1}-potent matrix are considered. First, we study the existence of the solutions of the associated inverse eigenvalue problem and present an explicit form for them. Then, when such a solution exists, an expression for the solution to the corresponding optimal approximation problem is obtained.
A nonlinear eigenvalue problem for the periodic scalar p-Laplacian
2014
We study a parametric nonlinear periodic problem driven by the scalar $p$-Laplacian. We show that if $\hat \lambda_1 >0$ is the first eigenvalue of the periodic scalar $p$-Laplacian and $\lambda> \hat \lambda_1$, then the problem has at least three nontrivial solutions one positive, one negative and the third nodal. Our approach is variational together with suitable truncation, perturbation and comparison techniques.
Existence and gap-bifurcation of multiple solutions to certain nonlinear eigenvalue problems
1993
IN THIS PAPER we study: (i) a class of operator equations in an abstract Hilbert space; and (ii) the L2-theory of certain nonlinear Schrodinger equations which can be viewed as special cases of (i). In order to describe the type of abstract nonlinear eigenvalue problems to be discussed, consider a real Hilbert space H with scalar product (* , *) and norm II.11 and let S be a (not necessarily bounded) positive self-adjoint linear operator in li. We write S in the form
Nonlinear Eigenvalue Problems of Schrödinger Type Admitting Eigenfunctions with Given Spectral Characteristics
2002
The following work is an extension of our recent paper [10]. We still deal with nonlinear eigenvalue problems of the form in a real Hilbert space ℋ with a semi-bounded self-adjoint operator A0, while for every y from a dense subspace X of ℋ, B(y ) is a symmetric operator. The left-hand side is assumed to be related to a certain auxiliary functional ψ, and the associated linear problems are supposed to have non-empty discrete spectrum (y ∈ X). We reformulate and generalize the topological method presented by the authors in [10] to construct solutions of (∗) on a sphere SR ≔ {y ∈ X | ∥y∥ℋ = R} whose ψ-value is the n-th Ljusternik-Schnirelman level of ψ| and whose corresponding eigenvalue is t…
Interior Eigenvalue Density of Jordan Matrices with Random Perturbations
2017
International audience; We study the eigenvalue distribution of a large Jordan block subject to a small random Gaussian perturbation. A result by E. B. Davies and M. Hager shows that as the dimension of the matrix gets large, with probability close to 1, most of the eigenvalues are close to a circle.We study the expected eigenvalue density of the perturbed Jordan block in the interior of that circle and give a precise asymptotic description.; Nous étudions la distribution de valeurs propres d’un grand bloc de Jordan soumis à une petite perturbation gaussienne aléatoire. Un résultat de E. B. Davies et M. Hager montre que quand la dimension de la matrice devient grande, alors avec probabilité…