Publications related to Toeplitz matrix

RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...

Siam Publications2024

A model for the consolidation of hybrid textiles considering air entrapment, dissolution and diffusion

Véronique Michaud, Vincent Werlen, Christian Rytka

A new model is proposed for the consolidation of hybrid textiles, in which air entrapment and dissolution are considered. One of the key parameters is tow permeability, which is described by the analytical model of Gebart and validated at very high fibre v ...

ELSEVIER SCI LTD2023

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022

Iterative refinement of Schur decompositions

Daniel Kressner, Zvonimir Bujanovic

The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

SPRINGER2023

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Daniel Kuhn, Tobias Sutter, Wouter Jongeneel

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

2023

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

2021

Description of beam instabilities in synchrotrons with wakefields and space charge forces using the circulant matrix model

Xavier Buffat, Tatiana Pieloni, Adrian Oeftiger

A new model for the description of beam instabilities in synchrotrons featuring wakefields and space charge forces is proposed, using the circulant matrix approach. The predictions of this model are discussed in light of past ones, with a particular emphas ...

2021

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

David Valentin Strütt

In this thesis, we study two distinct problems. The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...

EPFL2018

A New Look at Civic Design: Park Systems in America

Matthew Skjonsberg

A New Look at Civic Design reflects on the nature of the various crises facing the very idea of democracy today, explicitly in relation to climate change - namely mass extinctions, water scarcity and overabundance, and in general widespread and increasing ...

EPFL2018

Robust and Efficient Data Clustering with Signal Processing on Graphs

Lionel Jérémie Martin

Data is pervasive in today's world and has actually been for quite some time. With the increasing volume of data to process, there is a need for faster and at least as accurate techniques than what we already have. In particular, the last decade recorded t ...

EPFL2018

Extension complexity of stable set polytopes of bipartite graphs

Yuri Faenza, Manuel Francesco Aprile

The extension complexity xc(P) of a polytope P is the minimum number of facets of a polytope that affinely projects to P. Let G be a bipartite graph with n vertices, m edges, and no isolated vertices. Let STAB(G) be the convex hull of the stable sets of G. ...

Springer2017

An experimentalist's guide to the matrix element in angle resolved photoemission

Simon Karl Moser

Angle resolved photoemission spectroscopy (ARPES) is commonly known as a powerful probe of the one-electron removal spectral function in ordered solid state. With increasing efficiency of light sources and spectrometers, experiments over a wide range of em ...

Elsevier Science Bv2017

A block algorithm for computing antitriangular factorizations of symmetric matrices

Daniel Kressner, Zvonimir Bujanovic

Any symmetric matrix can be reduced to antitriangular form in finitely many steps by orthogonal similarity transformations. This form reveals the inertia of the matrix and has found applications in, e.g., model predictive control and constraint preconditio ...

Springer2016

ALS Scheme using Extent-based Constraints for the Analysis of Chemical Reaction Systems

Dominique Bonvin, Julien Léo Billeter, Michael Amrhein

Multivariate curve resolution via alternating least squares (ALS) is used to resolve the concentration profiles C and the pure component spectra E of S species from the multivariate absorbance data A, assuming the bilinear model ...

2016

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta

We present a theoretical analysis and comparison of the effect of

ℓ _{ 1 }

versus

ℓ _{ 2 }

regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the s ...

IEEE2016

Hopfield neural network deconvolution for weak lensing measurement

Frédéric Courbin, Georges Meylan, Malte Tewes, Guldariya Nurbaeva

Weak gravitational lensing has the potential to place tight constraints on the equation of the state of dark energy. However, this will only be possible if shear measurement methods can reach the required level of accuracy. We present a new method for meas ...

EDP Sciences2015

Approximate Matrix Multiplication with Application to Linear Embeddings

Anastasios Kyrillidis, Michail Vlachos

In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as the ratio of th ...

Ieee2014

Impact of tunneling anisotropy on the conductivity of nanorod dispersions

Claudio Grimaldi, Biagio Nigro

While the tunneling conductance between two spherical-like conducting particles depends on the relative interparticle distance, the wave function overlap between states of two rodlike particles, and so the tunneling conductance, depends also on the relativ ...

American Physical Society2014

Structured Canonical Forms For Products Of (Skew-) Symmetric Matrices And The Matrix Equation XAX = B

Daniel Kressner, Xin Liu

The contragredient transformation A bar right arrow P-1 AP-(inverted perpendicular) , B bar right arrow P-inverted perpendicular BP of two matrices A, B effects simultaneous similarity transformations of the products AB and BA. This work provides structure ...

Int Linear Algebra Soc2013

Analytical shape derivatives of the MFIE system matrix discretized with RWG functions

Juan Ramon Mosig, Athanasios Polymeridis

An analytical formula for the shape derivative of the magnetic field integral equation (MFIE) method of moments (MoM) system matrix (or impedance matrix) is derived and validated against finite difference formulas. The motivation for computing the shape de ...

Institute of Electrical and Electronics Engineers2013