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

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Alexandre Caboussat, Dimitrios Gourzoulidis

In this article, we address the numerical solution of the Dirichlet problem for the three-dimensional elliptic Monge-Ampere equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators fro ...

SPRINGER/PLENUM PUBLISHERS2018

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Volkan Cevher, Junhong Lin

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regressi ...

2018

Smoothing Alternating Direction Methods for Fully Nonsmooth Constrained Convex Optimization

Volkan Cevher, Quoc Tran Dinh

We propose two new alternating direction methods to solve “fully” nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and feasibility gap ...

Springer2018

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

Fabio Nobile, Giovanni Migliorati

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

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

MATHICSE Technical Report : Multilevel weighted least squares polynomial approximation

Fabio Nobile

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...

MATHICSE2017

Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression

Nicolas Henri Bernard Flammarion, Aymeric Daphnis Kévin Dieuleveut

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first algorithm that a ...

2017

Reconstruction of 3D scattered data via radial basis functions by efficient and robust techniques

Alberto Crivellaro

We propose new algorithms to overcome two of the most constraining limitations of surface reconstruction methods in use. In particular, we focus on the large amount of data characterizing standard acquisitions by scanner and the noise intrinsically introdu ...

Elsevier Science Bv2017

A Functional Framework for Enhanced Ultrasound Imaging

Ultrasound systems are cheap, portable, and fast, which have become impressively popular over the last decades. State-of art imaging is however known to be sub-optimal. Most attempts to improve it formulate the problem on a discrete spatial grid and suffer ...

2017

Case Study of Data Assimilation Methods with the LWR-Proteus Phase II Experimental Campaign

Andreas Pautz, Mathieu Hursin, Daniel Jerôme Siefman

This paper describes the application of data assimilation methods to CASMO-5 simulations of a Proteus research reactor experiment. Its focus is a comparison and evaluation of three prominent data assimilation methods: generalized linear least squares, MOCA ...

2017

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

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A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Smoothing Alternating Direction Methods for Fully Nonsmooth Constrained Convex Optimization

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

Sampling at unknown locations, with an application in surface retrieval

MATHICSE Technical Report : Multilevel weighted least squares polynomial approximation

Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression

Reconstruction of 3D scattered data via radial basis functions by efficient and robust techniques

A Functional Framework for Enhanced Ultrasound Imaging

Case Study of Data Assimilation Methods with the LWR-Proteus Phase II Experimental Campaign

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Sampling at unknown locations, with an application in surface retrieval

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

Smoothing Alternating Direction Methods for Fully Nonsmooth Constrained Convex Optimization

Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression

MATHICSE Technical Report : Multilevel weighted least squares polynomial approximation

Reconstruction of 3D scattered data via radial basis functions by efficient and robust techniques

A Functional Framework for Enhanced Ultrasound Imaging

Case Study of Data Assimilation Methods with the LWR-Proteus Phase II Experimental Campaign