English
Related papers

Related papers: Cross-Gramian-Based Dominant Subspaces

200 papers

The quadrature-based balanced truncation (QuadBT) framework of arXiv:2104.01006 is a non-intrusive reformulation of balanced truncation (BT), a classical projection-based model-order reduction technique for linear systems. QuadBT is…

Numerical Analysis · Mathematics 2025-08-26 Sean Reiter , Ion Victor Gosea , Serkan Gugercin

We present a new method of modelling numerical systems where there are two distinct output solution classes, for example tipping points or bifurcations. Gaussian process emulation is a useful tool in understanding these complex systems and…

Methodology · Statistics 2022-12-08 Louise Kimpton , Peter Challenor , Daniel Williamson

Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…

Methodology · Statistics 2025-09-16 Xiaoyu Zhang , Di Wang , Guodong Li , Defeng Sun

This paper proposes a balancing-based model reduction approach for an interconnection of passive dynamic subsystems. This approach preserves the passivity and stability of both the subsystems and the interconnected system. Hereto, one…

Systems and Control · Electrical Eng. & Systems 2023-11-23 Luuk Poort , Bart Besselink , Rob H. B. Fey , Nathan van de Wouw

We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel…

Optimization and Control · Mathematics 2020-08-28 Simon Becker , Lorenz Richter

Dynamic evolution behaviors of dimension-varying control systems often appear in the genetic regulatory network and the vehicle clutch system etc. An interesting and significant study on dimension-varying control systems is how to realize…

Optimization and Control · Mathematics 2023-03-02 Naqi Fan , Lijun Zhang

We derive error bounds for CUR matrix approximation using determinant-based methods that relate local projection errors to global approximation quality. For general matrices, we establish determinant identities for bordered Gramian matrices…

Numerical Analysis · Mathematics 2026-03-05 Frank de Hoog , Markus Hegland

Feedback optimization is an increasingly popular control paradigm to optimize dynamical systems, accounting for control objectives that concern the system operation at steady-state. Existing feedback optimization techniques heavily rely on…

Optimization and Control · Mathematics 2025-04-08 Amir Mehrnoosh , Gianluca Bianchin

Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…

Optimization and Control · Mathematics 2023-10-05 Haoyue Wang , Promit Ghosal , Rahul Mazumder

In this paper, we tackle the problem of multi-cell resource scheduling, where the objective is to maximize the weighted sum-rate through inter-cell interference coordination (ICIC). The blanking method is used to mitigate the inter-cell…

Networking and Internet Architecture · Computer Science 2014-11-03 Akram Bin Sediq , Rainer Schoenen , Halim Yanikomeroglu , Gamini Senarath

Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global…

Numerical Analysis · Mathematics 2020-03-16 Adi Ditkowski , Sigal Gottlieb , Zachary J. Grant

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…

Numerical Analysis · Mathematics 2019-09-11 Marie Billaud-Friess , Anthony Nouy

Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized (stochastic) partial differential equations and hence reduce computational complexity. A particular class of MOR techniques is balancing…

Optimization and Control · Mathematics 2019-03-29 Martin Redmann

A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…

Strongly Correlated Electrons · Physics 2007-05-23 Tsuyoshi Kashima , Masatoshi Imada

Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…

Systems and Control · Electrical Eng. & Systems 2022-01-12 Federico Celi , Fabio Pasqualetti

Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…

Methodology · Statistics 2021-09-02 Rahul Ghosal , Sujit K. Ghosh

This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or…

Numerical Analysis · Mathematics 2023-07-24 Cecilia Pagliantini , Federico Vismara

In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…

Statistics Theory · Mathematics 2025-12-05 Kangqiang Li , Bingqi Liu , Yang Yang , Li Wang

The paper introduces a methodology for visualizing on a dimension reduced subspace the classification structure and the geometric characteristics induced by an estimated Gaussian mixture model for discriminant analysis. In particular, we…

Methodology · Statistics 2015-08-10 Luca Scrucca

Solving structured systems of linear equations in a non-centralized fashion is an important step in many distributed optimization and control algorithms. Fast convergence is required in manifold applications. Known decentralized algorithms,…

Optimization and Control · Mathematics 2021-09-03 Alexander Engelmann , Timm Faulwasser