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 ...
Springer2024Dynamically 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 ...
2023Collaborative 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 ...
2021On 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 HEIDELBERG2020Wavelet 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 ...
2020Rational Krylov for Stieltjes matrix functions: convergence and pole selection
Evaluating the action of a matrix function on a vector, that is , is an ubiquitous task in applications. When is large, one usually relies on Krylov projection methods. In this paper, we provide effective choices for the pole ...
2019On 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 AG2018Low-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 ...
2018Method, 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 ...
2018Structure 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