11 citations · 23 across the 13 of their papers we have counts for
14 papers
On a family of low-rank algorithms for large-scale algebraic Riccati equations
Christian Bertram, Heike Faßbender
In [3] it was shown that four seemingly different algorithms for computing low-rank approximate solutions to the solution of large-scale continuous-time algebraic Riccati…
The Hamiltonian Extended Krylov Subspace Method
Peter Benner, Heike Faßbender, Michel-Niklas Senn
An algorithm for constructing a -orthogonal basis of the extended Krylov subspace $H^{2r-1}u, H^{-1}u, H^{-2}u,…
A rational Even-IRA algorithm for the solution of T-even polynomial eigenvalue problems
Peter Benner, Heike Fassbender, Philip Saltenberger
In this work we present a rational Krylov subspace method for solving real large-scale polynomial eigenvalue problems with T-even (that is, symmetric/skew-symmetric) structure. Our…
Riccati ADI: Existence, uniqueness and new iterative methods
Christian Bertram, Heike Faßbender
The approximate solution of large-scale algebraic Riccati equations is considered. We are interested in approximate solutions which yield a Riccati residual matrix of a particular…
Nearly optimal scaling in the SR decomposition
Heike Fassbender, Miroslav Rozloznik, Sanja Singer
In this paper we analyze the nearly optimal block diagonal scalings of the rows of one factor and the columns of the other factor in the triangular form of the SR decomposition. Th…
A link between gramian based model order reduction and moment matching
Christian Bertram, Heike Faßbender
We analyze a family of Runge-Kutta based quadrature algorithms for the approximation of the gramians of linear time invariant dynamical systems. The approximated gramians are used…
Simultaneous hollowisation, joint numerical range, and stabilization by noise
Tobias Damm, Heike Fassbender
We consider orthogonal transformations of arbitrary square matrices to a form where all diagonal entries are equal. In our main results we treat the simultaneous transformation of…
A note on the singular value decomposition of (skew-)involutory and (skew-)coninvolutory matrices
Heike Faßbender, Martin Halwaß
The singular values of an involutory matrix appear in pairs while the singular values may appear in pairs or by themselves.…
Lyapunov and Sylvester equations: A quadrature framework
Christian Bertram, Heike Faßbender
This paper introduces a novel framework for the solution of (large-scale) Lyapunov and Sylvester equations derived from numerical integration methods. Suitable systems of ordinary…
On normal and structured matrices under unitary structure-preserving transformations
Erna Begovic, Heike Fassbender, Philip Saltenberger
Structured canonical forms under unitary and suitable structure-preserving similarity transformations for normal and (skew-)Hamiltonian as well as normal and per(skew)-Hermitian ma…
On a new kind of Ansatz Spaces for Matrix Polynomials
Heike Fassbender, Philip Saltenberger
In this paper, we introduce a new family of equations for matrix pencils that may be utilized for the construction of strong linearizations for any square or rectangluar matrix pol…
On vector spaces of linearizations for matrix polynomials in orthogonal bases
Heike Faßbender, Philip Saltenberger
Matrix polynomials given in an orthogonal basis are considered. Following the ideas of Mackey et al. "Vector spaces of Linearizations for Matrix Polynomials" (2006), the vec- tor s…
Symmetric and skew-symmetric block-Kronecker linearizations
Heike Faßbender, Javier Perez, Nikta Shayanfar
Many applications give rise to structured matrix polynomials. The problem of constructing structure-preserving strong linearizations of structured matrix polynomials is revisited i…
Preconditioned Iterative Solves in Model Reduction of Second Order Linear Dynamical Systems
Navneet Pratap Singh, Kapil Ahuja, Heike Fassbender
Recently a new algorithm for model reduction of second order linear dynamical systems with proportional damping, the Adaptive Iterative Rational Global Arnoldi (AIRGA) algorithm, h…