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Deflation in Krylov subspace methods and distance to uncontrollability

Daniel Kressner

The task of extracting from a Krylov decomposition the approximation to an eigenpair that yields the smallest backward error can be phrased as finding the smallest perturbation which makes an associated matrix pair uncontrollable. Exploiting this relations ...

2007

On the stability of Reduced Basis methods for Stokes Equations in parametrized domains

Gianluigi Rozza

We present an application of reduced basis method for Stokes equations in domains with affine parametric dependence. The essential components of the method are (i) the rapid convergence of global reduced basis approximations – Galerkin projection onto a sp ...

2007

VLSI implementation of a high-speed iterative sorted MMSE QR decomposition

Andreas Peter Burg

The QR decomposition is an important, but often underestimated prerequisite for pseudo- or non-linear detection methods such as successive interference cancellation or sphere decoding for multiple-input multiple-output (MIMO) systems. The ability of concur ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2007

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

Structured Eigenvalue Problems

Daniel Kressner

Most eigenvalue problems arising in practice are known to be structured. Structure is often introduced by discretization and linearization techniques but may also be a consequence of properties induced by the original problem. Preserving this structure can ...

2006

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

Multishift variants of the QZ algorithm with aggressive early deflation

Daniel Kressner, Bo Kågström

New variants of the QZ algorithm for solving the generalized eigenvalue problem are proposed. An extension of the small-bulge multishift QR algorithm is developed, which chases chains of many small bulges instead of only one bulge in each QZ iteration. Thi ...

Society for Industrial and Applied Mathematics2006

Structured eigenvalue condition numbers

Daniel Kressner

This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to structures that form Jordan algebras, Lie algebras, and automorphism gro ...

Society for Industrial and Applied Mathematics2006

Structure-preserving eigenvalue solvers for robust stability and controllability estimates

Daniel Kressner

Structured eigenvalue problems feature a prominent role in many algorithms for the computation of robust measures for the stability or controllability of a linear control system. Structures that typically arise are Hamiltonian, skew-Hamiltonian, and symple ...

IEEE2006

Finding the distance to instability of a large sparse matrix

Daniel Kressner

The distance to instability of a matrix A is a robust measure for the stability of the corresponding dynamical system x = Ax, known to be far more reliable than checking the eigenvalues of A. In this paper, a new algorithm for computing such a distance is ...

IEEE2006