Publications related to Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

We analyze the accuracy of the discrete least-squares approximation of a function

u

in multivariate polynomial spaces

P_\Lambda:=span\{y\mapsto y^\nu \,: \, \nu\in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma:=[-1,1]^d

, based on the s ...

2017

Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy

Martin Vetterli, Thierry Blu, Hanjie Pan

It is a classic problem to estimate continuous-time sparse signals, like point sources in a direction-of-arrival problem, or pulses in a time-of-flight measurement. The earliest occurrence is the estimation of sinusoids in time series using Prony's method. ...

Institute of Electrical and Electronics Engineers2017

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

Handheld reflectance acquisition of paintings

Martin Vetterli, Sabine Süsstrunk, Loïc Arnaud Baboulaz, Damien Firmenich, Niranjan Thanikachalam

Relightable photographs are alternatives to traditional photographs as they provide a richer viewing experience. However, the complex acquisition systems of existing techniques have restricted its usage to specialized setups. We introduce an easy-to-use an ...

Ieee-Inst Electrical Electronics Engineers Inc2017

Riemannian Optimization For High-Dimensional Tensor Completion

Michael Maximilian Steinlechner

Tensor completion aims to reconstruct a high-dimensional data set where the vast majority of entries is missing. The assumption of low-rank structure in the underlying original data allows us to cast the completion problem into an optimization problem rest ...

Siam Publications2016

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Frank de Zeeuw

Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...

Duke Univ Press2016

Design and quality evaluation of micro-optical freeform beam shapers

Hans Peter Herzig, Daniel Infante Gómez

A method to generate thin micro-optical freeform (MOF) beam shapers by wrapping a much thicker freeform surface is provided. The influence of parameters such as the clipping factor q, the design wavelength and the spectrum of the light source into the qual ...

2016

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...

2015

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

Giovanni Migliorati

We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is ...

Elsevier2015

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate func- tions based on random sampling according to a given probability measure. Recent work has shown th ...

MATHICSE2014

Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties

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Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy

Distinct distances on regular varieties over finite fields

Handheld reflectance acquisition of paintings

Riemannian Optimization For High-Dimensional Tensor Completion

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Design and quality evaluation of micro-optical freeform beam shapers

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Distinct distances on regular varieties over finite fields

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

Handheld reflectance acquisition of paintings

Riemannian Optimization For High-Dimensional Tensor Completion

Design and quality evaluation of micro-optical freeform beam shapers

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES