Publications related to 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

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

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

Method and apparatus for multiple object tracking with k-shortest paths

Pascal Fua, François Fleuret, Jérôme Berclaz

Trajectories of objects are estimated by determining the optimal solution(s) of a tracking model on the basis of an occupancy probability distribution. The occupancy probability distribution is the probability of presence of objects over a set of discrete ...

2013

Noncontacting benchtop measurements of the elastic properties of shales

Thomas Emmanuel Blum

We evaluated a laser-based noncontacting method to measure the elastic anisotropy of horizontal shale cores. Whereas conventional transducer data contained an ambiguity between phase and group velocity measurements, small laser source and receiver footprin ...

2013

Randomized Extended Kaczmarz For Solving Least Squares

Nikolaos Freris

We present a randomized iterative algorithm that exponentially converges in the mean square to the minimum l(2)-norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to obtain an estimate o ...

Society for Industrial and Applied Mathematics2013

Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

Sabine Burgdorf

This paper presents an algorithm and its implementation in the software package NCSOStools for finding sums of Hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of t ...

Springer2013

Modelling the effect of size on the aerial dispersal of microorganisms

Edward Mitchell, Isabelle Bey, Symeon Koumoutsaris

Aim We investigate the long-standing question of whether the small size of microbes allows most microbial species to colonize all suitable sites around the globe or whether their ranges are limited by opportunities for dispersal. In this study we use a mod ...

2012

Compressible distributions for high-dimensional statistics

Volkan Cevher, Rémi Gribonval

We develop a principled way of identifying probability distributions whose independent and identically distributed realizations are compressible, i.e., can be well approximated as sparse. We focus on Gaussian compressed sensing, an example of underdetermin ...

Institute of Mathematical Statistics2012

Metastability of reversible condensed zero range processes on a finite set

Johel Beltran Ramirez

Let r : S x S -> R+ be the jump rates of an irreducible random walk on a finite set S, reversible with respect to some probability measure m. For alpha > 1, let g : N -> R+ be given by g(0) = 0, g(1) = 1, g(k) = (k/k - 1)(alpha), k >= 2. Consider a zero ra ...

2012

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

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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

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Method and apparatus for multiple object tracking with k-shortest paths

Noncontacting benchtop measurements of the elastic properties of shales

Randomized Extended Kaczmarz For Solving Least Squares

Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

Modelling the effect of size on the aerial dispersal of microorganisms

Compressible distributions for high-dimensional statistics

Metastability of reversible condensed zero range processes on a finite set

Method and apparatus for multiple object tracking with k-shortest paths

Metastability of reversible condensed zero range processes on a finite set

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Noncontacting benchtop measurements of the elastic properties of shales

Randomized Extended Kaczmarz For Solving Least Squares

Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

Modelling the effect of size on the aerial dispersal of microorganisms

Compressible distributions for high-dimensional statistics

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