Publications associées à Rang (algèbre linéaire)

Koopman-based Data-driven Robust Control of Nonlinear Systems Using Integral Quadratic Constraints

This paper introduces a novel method for data-driven robust control of nonlinear systems based on the Koopman operator, utilizing Integral Quadratic Constraints (IQCs). The Koopman operator theory facilitates the linear representation of nonlinear system d ...

2024

Unlabeled Principal Component Analysis and Matrix Completion

Yunzhen Yao, Liangzu Peng

We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...

Microtome Publishing2024

Less Conservatism, Stronger Robustness: Iterative Robust Gain-Scheduled Path Following Control of Autonomous Bus With Unstructured and Changing Dynamics

Denis Gillet, Man Shi, Jianwei Li

Path-following control is a critical technology for autonomous vehicles. However, time-varying parameters, parametric uncertainties, external disturbances, and complicated environments significantly challenge autonomous driving. We propose an iterative rob ...

Ieee-Inst Electrical Electronics Engineers Inc2024

Random matrix methods for high-dimensional machine learning models

Antoine Philippe Michel Bodin

In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

EPFL2024

T-5 configurations and hyperbolic systems

Carl Johan Peter Johansson, Riccardo Tione

In this paper, we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in [B. Kirchheim, S. Muller and V. S(sic)ver & aacute;k, Studying Nonlinear PDE by ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Preconditioning techniques for generalized Sylvester matrix equations

Yannis Dirk Voet

Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they now arise in an increasingly large number of applications. In this work, we consider algebraic parame ...

2023

A Determinantal Identity for the Permanent of a Rank 2 Matrix

Adam Wade Marcus

We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that t ...

TAYLOR & FRANCIS INC2022

A convex set of robust D—stabilizing controllers using Cauchy's argument principle

Alireza Karimi, Philippe Louis Schuchert

A new approach is presented to obtain a convex set of robust D—stabilizing fixed structure controllers, relying on Cauchy's argument principle. A convex set of D—stabilizing controllers around an initial D—stabilizing controller for a multi-model set is re ...

Elsevier2022

Identifiability and Generalizability from Multiple Experts in Inverse Reinforcement Learning

Volkan Cevher, Paul Thierry Yves Rolland, Luca Viano, Boris Nikolov

While Reinforcement Learning (RL) aims to train an agent from a reward function in a given environment, Inverse Reinforcement Learning (IRL) seeks to recover the reward function from observing an expert’s behavior. It is well known that, in general, variou ...

2022

Multiplicity-free representations of algebraic groups II

Donna Testerman, Martin W. Liebeck

We continue our work, started in [9], on the program of classifying triples (X, Y, V), where X, Yare simple algebraic groups over an algebraically closed field of characteristic zero with X < Y, and Vis an irreducible module for Y such that the restriction ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

SPRINGER HEIDELBERG2022

Testing For The Rank Of A Covariance Operator

Victor Panaretos

How can we discern whether the covariance operator of a stochastic pro-cess is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional dat ...

INST MATHEMATICAL STATISTICS-IMS2022

A unifying framework for form-finding and topology-finding of tensegrity structures

Yafeng Wang

This paper presents a unifying framework for the form-finding and topology-finding of tensegrity structures. The novel computational framework is based on rank-constrained linear matrix inequalities. For form-finding, given the topology (i.e., member conne ...

PERGAMON-ELSEVIER SCIENCE LTD2021

Sampling Geometry and Colour

Michalina Wanda Pacholska

In this thesis, we take a signal-processing approach to two research areas outside of the core of the signal processing research: geometry reconstruction and light propagation through non-uniform media. In the first area, we consider new sampling schemes ...

EPFL2021

Form-finding of tensegrity structures via rank minimization of force density matrix

Yafeng Wang

This study proposes a general computational framework for the form-finding of tensegrity structures. The procedure is divided into two stages in which the member force densities and nodal coordinates are obtained respectively. In the first stage, the deter ...

ELSEVIER SCI LTD2021

Mutual information for low-rank even-order symmetric tensor estimation

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method orig ...

OXFORD UNIV PRESS2021

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Daniel Kressner, Alice Cortinovis, Marcel Schweitzer

This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified conve ...

SIAM PUBLICATIONS2021

A first-order primal-dual method with adaptivity to local smoothness

Volkan Cevher, Maria-Luiza Vladarean

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

2021

Recursive blocked algorithms for linear systems with Kronecker product structure

Daniel Kressner

Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to higher-dimensional variants of g ...

SPRINGER2020

Sub-Matrix Factorization for Real-Time Vote Prediction

Patrick Thiran, Matthias Grossglauser, Victor Kristof

We address the problem of predicting aggregate vote outcomes (e.g., national) from partial outcomes (e.g., regional) that are revealed sequentially. We combine matrix factorization techniques and generalized linear models (GLMs) to obtain a flexible, effic ...

2020