Publications related to Orthogonal basis

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Siam Publications2024

Randomized flexible GMRES with deflated restarting

Laura Grigori, Emeric Martin

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

Spectral representation of EEG data using learned graphs with application to motor imagery decoding

Dimitri Nestor Alice Van De Ville, Hamid Behjat, Maliheh Miri

Electroencephalography (EEG) data entail a complex spatiotemporal structure that reflects ongoing organi-zation of brain activity. Characterization of the spatial patterns is an indispensable step in numerous EEG processing pipelines. We present a novel me ...

Oxford2023

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

Plane Waves Versus Correlation-Consistent Basis Sets: A Comparison of MP2 Non-Covalent Interaction Energies in the Complete Basis Set Limit

Ursula Röthlisberger, Justin Villard, Martin Peter Bircher

Second-order Moller-Plesset perturbation theory (MP2) is the most expedient wave function-based method for considering electron correlation in quantum chemical calculations and, as such, provides a cost-effective framework to assess the effects of basis se ...

Washington2023

A smooth basis for atomistic machine learning

Michele Ceriotti, Kevin Kazuki Huguenin-Dumittan, Filippo Bigi

Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighborhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to ...

AIP Publishing2022

Optimal radial basis for density-based atomic representations

Michele Ceriotti, Sergey Pozdnyakov, Jigyasa Nigam, Félix Benedito Clément Musil, Alexander Jan Goscinski

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

AIP Publishing2021

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

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Orthogonal basis

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Randomized flexible GMRES with deflated restarting

Spectral representation of EEG data using learned graphs with application to motor imagery decoding

Dynamically Orthogonal Approximation for Stochastic Differential Equations

Plane Waves Versus Correlation-Consistent Basis Sets: A Comparison of MP2 Non-Covalent Interaction Energies in the Complete Basis Set Limit

Harmonic decomposition of the trace of 1D transfer matrices in layered media

A smooth basis for atomistic machine learning

Optimal radial basis for density-based atomic representations

On compact representations of Voronoi cells of lattices

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Chat with Graph Search

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Randomized flexible GMRES with deflated restarting

Dynamically Orthogonal Approximation for Stochastic Differential Equations

Plane Waves Versus Correlation-Consistent Basis Sets: A Comparison of MP2 Non-Covalent Interaction Energies in the Complete Basis Set Limit

Spectral representation of EEG data using learned graphs with application to motor imagery decoding

Optimal radial basis for density-based atomic representations

Harmonic decomposition of the trace of 1D transfer matrices in layered media

A smooth basis for atomistic machine learning

On compact representations of Voronoi cells of lattices