Publications related to Adaptive polynomial approximation by means of random discrete least squares

MATHICSE Technical Report : 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 sa ...

MATHICSE2015

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

Fabio Nobile, Giovanni Migliorati

We analyze the stability and accuracy of discrete least squares on multivariate polynomial spaces to approximate a given function depending on a multivariate random variable uniformly distributed on a hypercube. The polynomial approximation is calculated s ...

2015

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

Fabio Nobile, Giovanni Migliorati

We analyze the stability and accuracy of discrete least squares on multivariate poly- nomial spaces to approximate a given function depending on a multivariate random variable uniformly distributed on a hypercube. The polynomial approximation is calculated ...

MATHICSE2015

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

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

2014

Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

2014

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

Michaël Unser, Julien René Pierre Fageot, Arash Amini

The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specif ...

Springer Birkhauser2014

A study of the spatio-temporal behaviour of bed load transport rate fluctuations

Joris Heyman

This thesis addresses the problem of a statistical description of the transport of sediment as bed load. It highlights the role of fluctuations arising during the transport process, and their impact on macroscopic averages. The results presented here are b ...

EPFL2014

Shortest-Weight Paths In Random Regular Graphs

Léo Hamed Amini

Consider a random regular graph with degree d and of size n. Assign to each edge an independent and identically distributed exponential random variable with mean one. In this paper we establish a precise asymptotic expression for the maximum number of edge ...

Siam Publications2014

The Squares of Montchoisy. Notes for a History of the Open Form in Geneva

Elena Cogato Lanza

This paper deals with the ambivalent character of the neighborhood «Squares Montchoisy» built in Geneva between 1929 and 1957. According to visual representations (photographs and drawings) disseminated by the architect Maurice Braillard, the project embod ...

2014

Adaptive polynomial approximation by means of random discrete least squares

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MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

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

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Perturbation analysis for the Darcy problem with log-normal permeability

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

A study of the spatio-temporal behaviour of bed load transport rate fluctuations

Shortest-Weight Paths In Random Regular Graphs

The Squares of Montchoisy. Notes for a History of the Open Form in Geneva

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

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

The Squares of Montchoisy. Notes for a History of the Open Form in Geneva

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Perturbation analysis for the Darcy problem with log-normal permeability

A study of the spatio-temporal behaviour of bed load transport rate fluctuations

Shortest-Weight Paths In Random Regular Graphs