Publications related to On Generalized Weighted Hilbert Matrices

Related publications (29)

Sparse random hypergraphs: non-backtracking spectra and community detection

We consider the community detection problem in a sparse q-uniform hypergraph G, assuming that G is generated according to the Hypergraph Stochastic Block Model (HSBM). We prove that a spectral method based on the non-backtracking operator for hypergraphs w ...

OXFORD UNIV PRESS2024

Spectral Estimators for High-Dimensional Matrix Inference

Farzad Pourkamali

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

EPFL2024

A mathematical theory for mass lumping and its generalization with applications to isogeometric analysis

Annalisa Buffa, Yannis Dirk Voet, Espen Sande

Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the solution of the li ...

2023

System and method for transcoding spectral data with task-based optimization via symmetric non-negative matrix factorization

Forrest Simon Webler

A computer-implemented method for reconstructing/recovering high-resolution visible light spectral data at a target resolution d, that comprises obtaining a configuration of a low- resolution multi-channel imaging sensor of resolution p, the configuration ...

2022

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Jean Louis-Alexandre Fornerod

The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...

EPFL2022

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

A generalized mountain-pass theorem: the existence of multiple critical points

Hans-Jörg Ruppen

We analyse the existence of multiple critical points for an even functional J : H -> R in the following context: the Hilbert space H can be split into an orthogonal sum H = Y circle plus Z in such a way that inf{J(u) : u is an element of Z and parallel to ...

Springer Heidelberg2016

Convergence of adaptive algorithms for constrained weakly convex optimization

Yurii Malitskyi, Volkan Cevher, Ahmet Alacaoglu

We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the

\tilde O(t^{-1/2})

rate of convergence for the squared norm of the gradient of Moreau envelope, ...

2021

Spectral methods for tempered fractional differential equations

Jan Sickmann Hesthaven

In this paper, we first introduce fractional integral spaces, which possess some features: (i) when 0 < α < 1, functions in these spaces are not required to be zero on the boundary; (ii)the tempered fractional operators are equivalent to the Riemann-Liouvi ...

2016

Many-body localization in a fragmented Hilbert space

Loïc Jean Pierre Herviou

We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than t ...

2021

Estimation in Functional Lagged Regression

Lukasz Kidzinski

The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-2 in applications. A spectral approach to the estima ...

Wiley-Blackwell2015

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Daniel Kressner, Stefano Massei

Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, t ...

SIAM PUBLICATIONS2020

Asymptotic bifurcation and second order elliptic equations on R-N

Charles Stuart

This paper deals with asymptotic bifurcation, first in the abstract setting of an equation G(u) = lambda u, where G acts between real Hilbert spaces and lambda is an element of R, and then for square-integrable solutions of a second order non-linear ellipt ...

Elsevier Science Bv2015

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a k x k submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix can a ...

ELSEVIER SCIENCE INC2020

Approximate Matrix Multiplication with Application to Linear Embeddings

Anastasios Kyrillidis, Michail Vlachos

In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as the ratio of th ...

Ieee2014

A Unifying Representer Theorem for Inverse Problems and Machine Learning

Michaël Unser

Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of measurements. The method is applicable whenever the problem is formulated as an optimization task. The standar ...

2021

Plenoptic Spherical Sampling

Pascal Frossard, Pierre Vandergheynst, Luigi Bagnato

We present a novel plenoptic sampling scheme that permits an efficient representation of the full light ray field in a space limited by a convex closed surface. We show that a convenient way to sample the light ray field around an observer consists in usin ...

2012

Frequency domain theory for functional time series: Variance decomposition and an invariance principle

Neda Mohammadi Jouzdani

This paper is concerned with frequency domain theory for functional time series, which are temporally dependent sequences of functions in a Hilbert space. We consider a variance decomposition, which is more suitable for such a data structure than the varia ...

INT STATISTICAL INST2020

The Two-Well Problem For Piecewise-Affine Maps

Bernard Dacorogna

In the two-well problem we look for a map u which satisfies Dirichlet boundary conditions and whose gradient Du assumes values in SO (2) A boolean OR SO (2) B = S-A boolean OR S-B, for two given invertible matrices A, B (an element of SO (2) A is of the fo ...

2012