Concept

Covariance and contravariance of vectors

Related publications (46)

Randomized flexible GMRES with deflated restarting

For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g. to the generaliz ...

Springer2024

Dynamically Orthogonal Approximation for Stochastic Differential Equations

Fabio Nobile, Yoshihito Kazashi, Fabio Zoccolan

In this paper, we set the mathematical foundations of the Dynamical Low Rank Approximation (DLRA) method for high-dimensional stochastic differential equations. DLRA aims at approximating the solution as a linear combination of a small number of basis vect ...

2023

Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

Rachid Guerraoui, Sadegh Farhadkhani, El Mahdi El Mhamdi, Le Nguyen Hoang, Sébastien Louis Alexandre Rouault, Arsany Hany Abdelmessih Guirguis

We study Byzantine collaborative learning, where n nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and f < n nodes can behave arbitrarily. We prove that collaborati ...

2021

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...

SPRINGER HEIDELBERG2020

Wavelet analysis of the Besov regularity of Levy white noise

Julien René Pierre Fageot, Shayan Aziznejad

We characterize the local smoothness and the asymptotic growth rate of the Levy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend known results in two ways. First, we obtain new bounds for the local smoothn ...

2020

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Stefano Massei

Evaluating the action of a matrix function on a vector, that is

x=f(\mathcal M)v

, is an ubiquitous task in applications. When

\mathcal M

is large, one usually relies on Krylov projection methods. In this paper, we provide effective choices for the pole ...

2019

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio & Voulgaris (2010) described a deterministic single-exponential time algorithm for the Closest Vector Problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given lattice and thus may need exponen ...

SPRINGER INTERNATIONAL PUBLISHING AG2018

Low-latency speaker spotting with online diarization and detection

Sébastien Marcel, Nicholas Evans

This paper introduces a new task termed low-latency speaker spotting (LLSS). Related to security and intelligence applications, the task involves the detection, as soon as possible, of known speakers within multi-speaker audio streams. The paper describes ...

2018

Method, system, and device for learned invariant feature transform for computer images

Pascal Fua, Vincent Lepetit, Kwang Moo Yi, Eduard Trulls Fortuny

A method for training a feature detector of an image processing device, including the steps of detecting features in the image to generate a score map, computing a center of mass on the score map to generate a location, extracting a patch from the image at ...

2018

Structure preserving model reduction of parametric Hamiltonian systems

Jan Sickmann Hesthaven, Babak Maboudi Afkham

While reduced-order models (ROMs) are popular for approximately solving large systems of differential equations, the stability of reduced models over long-time integration remains an open question. We present a greedy approach for ROM generation of paramet ...

2017

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