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Singular quadratic eigenvalue problems: linearization and weak condition numbers

Publications associées (61)

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The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes

Annalisa Buffa

We extend the mimetic finite difference (MFD) method to the numerical treatment of magnetostatic fields problems in mixed div-curl form for the divergence-free magnetic vector potential. To accomplish this task, we introduce three sets of degrees of freedo ...

Elsevier2011

Bifurcation and decay of solutions for a class of elliptic equations on R-N

Charles Stuart

We consider a class of nonlinear eigenvalue problems including equations such as −Δu(x) + q(x)u(x) + γ u(x)2 ξ(x)2 + u(x)2 u = λu(x) for x ∈ R , where γ > 0, q ∈ L∞(RN ) and ξ ∈ L2(RN ) are given and we are interested in eigenvalues λ ∈ R for which this eq ...

American Mathematical Society, P.O. Box 6248 Ms. Phoebe Murdock, Providence, Ri 02940 Usa2011

Graph Theory Meets Ab Initio Molecular Dynamics: Atomic Structures and Transformations at the Nanoscale

Wanda Andreoni, Fabio Pietrucci

Social permutation invariant coordinates are introduced describing the bond network around a given atom. They originate from the largest eigenvalue and the corresponding eigenvector of the contact matrix, are invariant under permutation of identical atoms, ...

2011

A block Newton method for nonlinear eigenvalue problems

Daniel Kressner

We consider matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. One of the most fundamental differences from the linear case is that distinct eigenvalues may have linearly dependent eigenvectors or even share the same eigenvector. Th ...

2009

Implicit QR algorithms for palindromic and even eigenvalue problems

Daniel Kressner

In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward st ...

Springer Verlag2009

BECOOL: Ballooning eigensolver with COOL finite elements

Jonathan Graves, Wilfred Anthony Cooper

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equati ...

2009

An exact solution for ideal dam-break floods on steep slopes

Christophe Ancey, Martin Rentschler

Dam-break floods on steep slopes occur in diverse settings. They may result from failure of either natural or man-made dams, and they have been responsible for the loss of thousands of lives [Costa, 1988]. Recent disasters resulting from dam-break floods o ...

American Geophysical Union2008

Control and Optimization Methods for Traffic Signal Control in Large-scale Congested Urban Road Networks

he problem of designing real-time traffic signal control strategies for large-scale congested urban road networks via suitable application of control and optimization methods is considered. Three alternative methodologies are proposed, all based on the sto ...

IEEE2007

Balancing sparse Hamiltonian eigenproblems

Daniel Kressner

Balancing a matrix by a simple and accurate similarity transformation can improve the speed and accuracy of numerical methods for computing eigenvalues. We describe balancing strategies for a large and sparse Hamiltonian matrix H. It is first shown how to ...

Elsevier2006

Algorithm 854: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices II

Daniel Kressner

This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices. The implemented algorithms are based on orthogonal symplectic decompositions, implying numerical backward stabilit ...

Association for Computing Machinery2006