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Singular quadratic eigenvalue problems: linearization and weak condition numbers

Publications associées (61)

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In this paper, we propose a novel preconditioned solver for generalized Hermitian eigenvalue problems. More specifically, we address the case of a definite matrix pencil , that is, A, B are Hermitian and there is a shift such that is definite. Our new meth ...

Springer2014

Given a nonsymmetric matrix A, we investigate the effect of perturbations on an invariant subspace of A. The result derived in this paper differs from Stewart's classical result and sometimes yields tighter bounds. Moreover, we provide norm estimates for t ...

Siam Publications2014

Low-Rank Tensor Methods With Subspace Correction For Symmetric Eigenvalue Problems

Daniel Kressner, André Uschmajew, Michael Maximilian Steinlechner

We consider the solution of large-scale symmetric eigenvalue problems for which it is known that the eigenvectors admit a low-rank tensor approximation. Such problems arise, for example, from the discretization of high-dimensional elliptic PDE eigenvalue p ...

Siam Publications2014

This work presents a new methodology for computing ground states of Bose-Einstein condensates based on finite element discretizations on two different scales of numerical resolution. In a preprocessing step, a low-dimensional (coarse) generalized finite el ...

Society for Industrial and Applied Mathematics2014

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 al ...

Siam Publications2014

A point-wise approach that can be used efficiently in the numerical solution of Electric Field Integral Equations is introduced. The algorithm is based on the so-called magic distance concept, which defines exactly the point-to-point equivalent of a four-d ...

Wiley-Blackwell2013

This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix-valued function is computationally expensive. ...

Springer Netherlands2012

A large portion of software is used for numerical computation in mathematics, physics and engineering. Among the aspects that make verification in this domain difficult is the need to quantify numerical errors, such as roundoff errors and errors due to the ...

2012

Linearization techniques for band structure calculations in absorbing photonic crystals

Daniel Kressner, Peter Cedric Effenberger

Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modele ...

2011

Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems

Daniel Kressner, Peter Cedric Effenberger

Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this wor ...

Springer-Verlag2011