19 citations · 49 across the 9 of their papers we have counts for
11 papers
Low-rank solutions to the stochastic Helmholtz equation
Adem Kaya, Melina A. Freitag
In this paper, we consider low-rank approximations for the solutions to the stochastic Helmholtz equation with random coefficients. A Stochastic Galerkin finite element method is u…
Solving the Parametric Eigenvalue Problem by Taylor Series and Chebyshev Expansion
Thomas Mach, Melina A. Freitag
We discuss two approaches to solving the parametric (or stochastic) eigenvalue problem. One of them uses a Taylor expansion and the other a Chebyshev expansion. The parametric eige…
Time-limited Balanced Truncation for Data Assimilation Problems
Josie König, Melina A. Freitag
Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian infe…
Optimization based model order reduction for stochastic systems
Martin Redmann, Melina A. Freitag
In this paper, we bring together the worlds of model order reduction for stochastic linear systems and -optimal model order reduction for deterministic systems. In pa…
Numerical Linear Algebra in Data Assimilation
Melina A. Freitag
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the…
Inexact methods for the low rank solution to large scale Lyapunov equations
Patrick Kürschner, Melina A. Freitag
The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit (LR-ADI) iteration are established numerical tools for computing low-rank solution facto…
A low-rank approach to the solution of weak constraint variational data assimilation problems
Melina A. Freitag, Daniel L. H. Green
Weak constraint four-dimensional variational data assimilation is an important method for incorporating data (typically observations) into a model. The linearised system arising wi…
Balanced truncation and singular perturbation approximation model order reduction for stochastically controlled linear systems
Martin Redmann, Melina A. Freitag
When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approxima…
GMRES convergence bounds for eigenvalue problems
Melina Freitag, Patrick Kürschner, Jennifer Pestana
The convergence of GMRES for solving linear systems can be influenced heavily by the structure of the right hand side. Within the solution of eigenvalue problems via inverse iterat…
The calculation of the distance to a nearby defective matrix
Melina A. Freitag, Alastair Spence
In this paper a new fast algorithm for the computation of the distance of a matrix to a nearby defective matrix is presented. The problem is formulated following Alam & Bora (Linea…
The Origin of Power-Law Emergent Scaling in Large Binary Networks
D. P. Almond, C. J. Budd, M. A. Freitag +3
In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based…