Conveners
Posters: Poster Session
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Posters: Poster Blitz
- Davide Palitta (Max Planck Institute for Dynamics of Complex Technical Systems)
PDE-constrained optimization problems arise in a broad number of applications. The resulting large-scale saddle-point systems are challenging to solve and acquiring a full solution is often infeasible. We present a new framework to find a low-rank approximation to the solution by reformulating the system into a system of Sylvester-like matrix equations. These matrix equations are subsequently...
Consider the algebraic Riccati equation
$$A^{*}X + XA + C^*C - XBB^{*}X = 0$$
with large and sparse $A\in \mathbb{C}^{n\times n}$ and $B\in \mathbb{C}^{n\times m}$, $C\in \mathbb{C}^{p\times n}$. The goal is to find an approximate solution $X$ such that the rank of the Riccati residual remains equal to $p$. A method to determine an approximate solution to Riccati equations with this rank...
A stochastic cubical tensor is a three-mode array (or hypermatrix) with nonnegative entries, whose $1$-mode fibers (i.e., columns) sum up to $1$. Such tensors appear in certain higher-order Markov chains and random walks with memory, exactly as stochastic matrices describe classical discrete Markov chains and random walks.
The interest in higher-order stochastic processes is significantly...
Graph (or network) analysis is concerned with knowledge discovery from graph data. Corresponding analysis methods usually have their roots in graph theory, matrix computations, and statistics.
A growing class of analysis algorithms consists of methods based on the graph's Laplacian matrix. These include traditional methods using Laplacian eigenvectors such as spectral partitioning, spectral...
Among other things, M.E.S.S. can solve Lyapunov and Riccati equations, and perform model reduction of systems in state space and structured differential algebraic form. While until version 1.0.1 the work focused on algebraic equations and autonomous differential Riccati equations (DREs), the latest release adds support also for non-autonomous DREs.
In the first place, the poster presented will give an overview on the matrix equations that appear in the low-rank parameter-dependent fluid-structure interaction (FSI) framework. In contrast to linear FSI problems, the equations that result after finite element discretization of parameter-dependent nonlinear FSI problems are not translatable to a single matrix equation. Such a discretization...
We deduce a procedure to use balanced truncation for parameter-dependent differential-algebraic systems. For this, we have to solve parameter-dependent Lyapunov equations. Since solving large-scale Lyapunov equations for every parameter leads to very high computational costs we utilize the reduced-basis method to get a reduced Lyapunov equation that we can solve instead. In order to use this...
Matrix equations and their solutions play a key role in several problems arising in science and engineering. Our primary focus lies on matrix equations appearing in model-order reduction problems, where several well-known procedures, such as balanced truncation and interpolation-based methods, can be set up in the matrix equations form. In the last five years, several model reduction schemes...
In system theory, the so-called system Gramian matrices are operators encoding certain properties of an underlying input-output system. Usually, these system Gramians are computed as solutions to matrix equations, such as the Lyapunov equation and Sylvester equation. This means, the solution to certain matrix equations coincides with these system Gramians. Now, if the system Gramians are...
The MORLAB, Model Order Reduction LABoratoy, toolbox [1] is a free and open source software solution in MATLAB and GNU Octave for linear model reduction problems. Providing system theoretic model order reduction methods, the basis of the highly efficient implementation is built by a large variety of dense matrix equation solvers based on iterative methods like the matrix sign function, Newton...
