Publications related to Factorization of polynomials

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

A set

R\subset \mathbb{N}

is called rational if it is well approximable by finite unions of arithmetic progressions, meaning that for every

\unicode[STIX]{x1D716}>0

there exists a set

B=\bigcup _{i=1}^{r}a_{i}\mathbb{N}+b_{i}

, where $a_{1},\ldots ,a_ ...

2019

Petersson inner products of weight-one modular forms

Maryna Viazovska

In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that ...

2019

Isogeometric Analysis of the electrophysiology in the human heart: Numerical simulation of the bidomain equations on the atria

Alfio Quarteroni, Luca Pegolotti

We consider Isogeometric Analysis (IGA) for the numerical solution of the electrophysiology of the atria, which in this work is modeled by means of the bidomain equations on thin surfaces. First, we consider the bidomain equations coupled with the Roger-Mc ...

ELSEVIER SCIENCE SA2019

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

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham

Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

AMER MATHEMATICAL SOC2018

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Damian Mateusz Straszak

Optimization is a fundamental tool in modern science. Numerous important tasks in biology, economy, physics and computer science can be cast as optimization problems. Consider the example of machine learning: recent advances have shown that even the most s ...

EPFL2018

Stable high-order randomized cubature formulae in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

2018

Distinct distances on regular varieties over finite fields

Van Thang Pham

In this paper we study some generalized versions of a recent result due to Covert, Koh, and Pi (2015). More precisely, we prove that if a subset in a regular variety satisfies vertical bar epsilon vertical bar >> q(d-1/2 + 1/k-1), then Delta(k,F)(epsilon) ...

Elsevier2017

Sampling at unknown locations, with an application in surface retrieval

Martin Vetterli, Benjamin Bejar Haro, Adam James Scholefield, Michalina Wanda Pacholska

We consider the problem of sampling at unknown locations. We prove that, in this setting, if we take arbitrarily many samples of a polynomial or real bandlimited signal, it is possible to find another function in the same class, arbitrarily far away from t ...

2017

Efficient Preconditioning of hp-FEM Matrices by Hierarchical Low-Rank Approximations

Jan Sickmann Hesthaven, Paolo Gatto

We introduce a preconditioner based on a hierarchical low-rank compression scheme of Schur complements. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated, to high precisi ...

Springer Verlag2017

Factorization of polynomials

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Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

Petersson inner products of weight-one modular forms

Isogeometric Analysis of the electrophysiology in the human heart: Numerical simulation of the bidomain equations on the atria

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

Four-Variable Expanders Over The Prime Fields

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Stable high-order randomized cubature formulae in arbitrary dimension

Distinct distances on regular varieties over finite fields

Sampling at unknown locations, with an application in surface retrieval

Efficient Preconditioning of hp-FEM Matrices by Hierarchical Low-Rank Approximations

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

Distinct distances on regular varieties over finite fields

Petersson inner products of weight-one modular forms

Isogeometric Analysis of the electrophysiology in the human heart: Numerical simulation of the bidomain equations on the atria

Four-Variable Expanders Over The Prime Fields

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Stable high-order randomized cubature formulae in arbitrary dimension

Sampling at unknown locations, with an application in surface retrieval

Efficient Preconditioning of hp-FEM Matrices by Hierarchical Low-Rank Approximations

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