Publications related to Condition number

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

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 PUBL2022

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

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 ...

SPRINGER2022

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 ...

ELSEVIER SCIENCE SA2021

Damage-driven strain localisation in networks of fibres: A computational homogenisation approach

Pablo Antolin Sanchez, Felipe Figueredo Rocha

In many applications, such as textiles, fibreglass, paper and several kinds of biological fibrous tissues, the main load-bearing constituents at the micro-scale are arranged as a fibre network. In these materials, rupture is usually driven by micro-mechani ...

2021

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

David Pfefferlé, Antoine Baillod, Ajay Kumar

The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the ...

IOP PUBLISHING LTD2020

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Condition number

Singular quadratic eigenvalue problems: linearization and weak condition numbers

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

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

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

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

Iterative refinement of Schur decompositions

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

Damage-driven strain localisation in networks of fibres: A computational homogenisation approach

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

High-order essentially nonoscillatory methods based on radial basis functions

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Chat with Graph Search

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

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Singular quadratic eigenvalue problems: linearization and weak condition numbers

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

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

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

Iterative refinement of Schur decompositions

Damage-driven strain localisation in networks of fibres: A computational homogenisation approach

High-order essentially nonoscillatory methods based on radial basis functions