Publications associées à Conditionnement (analyse numérique)

Singular quadratic eigenvalue problems: linearization and weak condition numbers

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

SPRINGER2023

On the symmetries in the dynamics of wide two-layer neural networks

Lénaïc Chizat

We consider the idealized setting of gradient flow on the population risk for infinitely wide two-layer ReLU neural networks (without bias), and study the effect of symmetries on the learned parameters and predictors. We first describe a general class of s ...

AMER INST MATHEMATICAL SCIENCES-AIMS2023

Stable parameterization of continuous and piecewise-linear functions

Michaël Unser, Alexis Marie Frederic Goujon, Joaquim Gonçalves Garcia Barreto Campos

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

2023

Iterative pre-conditioning for expediting the distributed gradient-descent method: The case of linear least-squares problem

Nirupam Gupta

This paper considers the multi-agent linear least-squares problem in a server-agent network architecture. The system comprises multiple agents, each with a set of local data points. The agents are connected to a server, and there is no inter-agent communic ...

PERGAMON-ELSEVIER SCIENCE LTD2022

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Nicolas Henri Bernard Flammarion

We consider the problem of sampling from a density of the form p(x) ? exp(-f (x) - g(x)), where f : Rd-+ R is a smooth function and g : R-d-+ R is a convex and Lipschitz function. We propose a new algorithm based on the Metropolis-Hastings framework. Under ...

Microtome Publishing2022

On Preconditioning of Decentralized Gradient-Descent When Solving a System of Linear Equations

Nirupam Gupta

This article considers solving an overdetermined system of linear equations in peer-to-peer multiagent networks. The network is assumed to be synchronous and strongly connected. Each agent has a set of local data points, and their goal is to compute a line ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Adaptive analysis-aware defeaturing

Ondine Gabrielle Chanon

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, ...

EPFL2022

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

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Riccardo Puppi

Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...

EPFL2022

BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines

Rafael Vazquez Hernandez

We present the construction of additive multilevel preconditioners, also known as BPX preconditioners, for the solution of the linear system arising in isogeometric adaptive schemes with (truncated) hierarchical B-splines. We show that the locality of hier ...

2021