Publications related to Dirichlet's approximation theorem

Adaptive Symplectic Model Order Reduction Of Parametric Particle-Based Vlasov-Poisson Equation

Jan Sickmann Hesthaven, Nicolò Ripamonti, Cecilia Pagliantini

. High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of para ...

AMER MATHEMATICAL SOC2023

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Daniel Kressner, Stefano Massei, Alice Cortinovis

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

SIAM PUBLICATIONS2022

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation

Alice Cortinovis

In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices. In the first part, we consider algorithms for building ...

EPFL2022

Model order reduction based on functional rational approximants for parametric PDEs with meromorphic structure

Davide Pradovera

Many engineering fields rely on frequency-domain dynamical systems for the mathematical modeling of physical (electrical/mechanical/etc.) structures. With the growing need for more accurate and reliable results, the computational burden incurred by frequen ...

EPFL2021

Optimal Adversarial Policies in the Multiplicative Learning System With a Malicious Expert

Negar Kiyavash, Seyed Jalal Etesami

We consider a learning system based on the conventional multiplicative weight ( MW) rule that combines experts' advice to predict a sequence of true outcomes. It is assumed that one of the experts is malicious and aims to impose the maximum loss on the sys ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Local approximation of the Maximum Cut in regular graphs

Etienne Michel François Bamas

This paper is devoted to the distributed complexity of finding an approximation of the maximum cut (MAXCUT) in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any communica ...

ELSEVIER2020

Machine learning of multiscale active force generation models for the efficient simulation of cardiac electromechanics

Alfio Quarteroni, Francesco Regazzoni

High fidelity (HF) mathematical models describing the generation of active force in the cardiac muscle tissue typically feature a large number of state variables to capture the intrinsically complex underlying subcellular mechanisms. With the aim of drasti ...

2020

Distributed sampling for rational approximation of the acoustic scattering of an airfoil

Francesca Bonizzoni, Davide Pradovera

In this paper we compute a reduced order model for a time‐harmonic external acoustic scattering problem with parametric frequency. The employed technique is minimal rational interpolation, an explicit moment‐matching method for Hilbert space‐valued meromor ...

2019

An Optimal Space Lower Bound for Approximating MAX-CUT

Mikhail Kapralov

We consider the problem of estimating the value of MAX-CUT in a graph in the streaming model of computation. At one extreme, there is a trivial 2-approximation for this problem that uses only O(log n) space, namely, count the number of edges and output hal ...

ASSOC COMPUTING MACHINERY2019

Local Approximation of the Maximum Cut in Regular Graphs

Etienne Michel François Bamas

This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any communication and ...

SPRINGER INTERNATIONAL PUBLISHING AG2019

On quadratic matrix equations with infinite size coefficients encountered in QBD stochastic processes

Stefano Massei

Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...

WILEY2018

Multi space reduced basis preconditioners for parametrized partial differential equations

Niccolò Dal Santo

The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...

EPFL2018

From Tarski's Plank Problem to Simultaneous Approximation

János Pach, Andrei Kupavskii

A slab (or plank) is the part of the d-dimensional Euclidean space that lies between two parallel hyperplanes. The distance between the these hyperplanes is called the width of the slab. It is conjectured that the members of any infinite family of slabs wi ...

Mathematical Assoc Amer2017

Simultaneous Approximation of Polynomials

János Pach, Andrei Kupavskii

Let P-d denote the family of all polynomials of degree at most d in one variable x, with real coefficients. A sequence of positive numbers x(1)

Springer Int Publishing Ag2016

Exact simulation of max-stable processes

Sebastian Engelke, Clément Dombry

Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are o ...

Oxford University Press2016

Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs

Fabio Nobile, Eleonora Musharbash

In this work we discuss the dynamically orthogonal (DO) approximation of time dependent partial differential equations with random data. The approximate solution is expanded at each time instant on a time dependent orthonormal basis in the physical domain ...

2015

Opaque Sets

János Pach

The problem of finding "small" sets that meet every straight-line which intersects a given convex region was initiated by Mazurkiewicz in 1916. We call such a set an opaque set or a barrier for that region. We consider the problem of computing the shortest ...

Springer2014

Recovering Neugebauer colorant reflectances and Ink-spreading curves from printed color images

Roger Hersch, Thomas Bugnon

Spectral reflection prediction models, although effective, are impractical for certain industrial applications such as self-calibrating devices and online monitoring because their calibration requires specific color-constant calibration patches. Using the ...

Wiley-Blackwell2014

On the finite section method for computing exponentials of doubly-infinite skew-Hermitian matrices

Meiyue Shao

Computing the exponential of large-scale skew-Hermitian matrices or parts thereof is frequently required in applications. In this work, we consider the task of extracting finite diagonal blocks from a doubly-infinite skew-Hermitian matrix. These matrices u ...

Elsevier Science Inc2014

Can Localization Microscopy Benefit From Approximation Theory?

Michaël Unser, Cédric René Jean Vonesch, Hagay Kirshner

We introduce a general and computationally efficient approach to 3-D localization microscopy. The main idea is to construct a continuous-domain representation of the PSF by expanding it in a polynomial B-spline basis. This allows us to fit the PSF to the d ...

IEEE2013