Related papers: Balanced Truncation via Tangential Interpolation
This paper presents a model reduction method for the class of linear quantum stochastic systems often encountered in quantum optics and their related fields. The approach is proposed on the basis of an interpolatory projection ensuring that…
When solving partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce…
This paper considers the problem of assumptions refinement in the context of unrealizable specifications for reactive systems. We propose a new counterstrategy-guided synthesis approach for GR(1) specifications based on Craig's…
This paper revisits the modal truncation from an optimisation point of view. In particular, the concept of dominant poles is formulated with respect to different systems norms as the solution of the associated optimal modal truncation…
Efficient and accurate low-rank approximation (LRA) methods are of great significance for large-scale data analysis. Randomized tensor decompositions have emerged as powerful tools to meet this need, but most existing methods perform poorly…
In this article we study the bivariate truncated moment problem (TMP) of degree $2k$ on the union of parallel lines. First we present an alternative proof of Fialkow's solution \cite{Fia15} to the TMP on the union of two parallel lines…
We consider equations involving the truncated laplacians and having lower order terms with singular potentials posed in punctured balls. We study both the principal eigenvalue problem and the problem of classification of solutions, in…
In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a…
Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is…
We discuss balanced truncation model order reduction for large-scale quadratic-bilinear (QB) systems. Balanced truncation for linear systems mainly involves the computation of the Gramians of the system, namely reachability and…
Toeplitz-structured linear systems arise often in practical engineering problems. Correspondingly, a number of algorithms have been developed that exploit Toeplitz structure to gain computational efficiency when solving these systems. The…
The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on…
In this paper, we introduce a novel low-rank Hankel tensor completion approach to address the problem of multi-measurement spectral compressed sensing. By lifting the multiple signals to a Hankel tensor, we reformulate this problem into a…
In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which…
The problems of optimal recovery of unbounded operators are studied. Optimality means the highest possible accuracy and the minimal amount of discrete information involved. It is established that the truncation method, when certain…
This paper addresses the problem of identifying linear systems from noisy input-output trajectories. We introduce Thresholded Ho-Kalman, an algorithm that leverages a rank-adaptive procedure to estimate a Hankel-like matrix associated with…
We propose a novel rank-adaptive higher-order orthogonal iteration (HOOI) algorithm to compute the truncated Tucker decomposition of higher-order tensors with a given error tolerance, and prove that the method is locally optimal and…
Model order reduction algorithms for large-scale descriptor systems are proposed using balanced truncation, in which symmetry or block skew symmetry (reciprocity) and the positive realness of the original transfer matrix are preserved. Two…
Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…
We investigate the problem of approximating the matrix function $f(A)$ by $r(A)$, with $f$ a Markov function, $r$ a rational interpolant of $f$, and $A$ a symmetric Toeplitz matrix. In a first step, we obtain a new upper bound for the…