Publications related to Spectrum (functional analysis)

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

New York2024

Explicit representations for Banach subspaces of Lizorkin distributions

Michaël Unser, Sebastian Jonas Neumayer

The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

A mixed precision LOBPCG algorithm

Daniel Kressner, Meiyue Shao, Yuxin Ma

The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A. In this work, we propose a mix ...

SPRINGER2023

Identifying Large Charge operators

Riccardo Rattazzi, Alexander Monin, Gil Badel

The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on U(1) invariant Wilson-Fisher fixed points, we study the spectrum of spinning l ...

SPRINGER2023

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the generalized eigenf ...

Philadelphia2023

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Daniel Kressner, Ivana Sain Glibic

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

Asymmetric phase modulation of light with parity-symmetry broken metasurfaces

Karim Achouri, Jean-Yves Duboz

The design of wavefront-shaping devices is conventionally approached using real-frequency modeling. However, since these devices interact with light through radiative channels, they are by default non-Hermitian objects having complex eigenvalues (poles and ...

Washington2023

Weak nonlinearity for strong non-normality

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière

We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they experience transient growth or respond to harmonic forcing. This approach reconciles the non-modal nature of ...

2022

Stochastic distributed learning with gradient quantization and double-variance reduction

Sebastian Urban Stich, Konstantin Mishchenko

We consider distributed optimization over several devices, each sending incremental model updates to a central server. This setting is considered, for instance, in federated learning. Various schemes have been designed to compress the model updates in orde ...

TAYLOR & FRANCIS LTD2022

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Spectrum (functional analysis)

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Explicit representations for Banach subspaces of Lizorkin distributions

A mixed precision LOBPCG algorithm

Identifying Large Charge operators

Représenter l'invention : Étude de l'évolution du dessin d'objet technique en Angleterre (ca. 1750-1850)

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Asymmetric phase modulation of light with parity-symmetry broken metasurfaces

Weak nonlinearity for strong non-normality

Stochastic distributed learning with gradient quantization and double-variance reduction

Graph Chatbot

Chat with Graph Search

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Explicit representations for Banach subspaces of Lizorkin distributions

A mixed precision LOBPCG algorithm

Identifying Large Charge operators

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Stochastic distributed learning with gradient quantization and double-variance reduction

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Asymmetric phase modulation of light with parity-symmetry broken metasurfaces

Représenter l'invention : Étude de l'évolution du dessin d'objet technique en Angleterre (ca. 1750-1850)

Weak nonlinearity for strong non-normality