Publications related to Stable high-order randomized cubature formulae in arbitrary dimension

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

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

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

Infection Spread In Random Geometric Graphs

Ghurumuruhan Ganesan

In this paper we study the speed of infection spread and the survival of the contact process in the random geometric graph G = G (n, r(n), f) of n nodes independently distributed in S = -1/2, 1/2 according to a certain density f(.). In the first part ...

Applied Probability Trust2015

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

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Alfio Quarteroni, Peng Chen

Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...

Elsevier Science Sa2013

Susceptibility of Electro-Explosive Devices to Microwave Interference

In this paper, the electromagnetic susceptibility of electro-explosive devices (EEDs) including their connection wires is assessed statistically. The electromagnetic coupling and the thermal power dissipation are modeled to determine the activation conditi ...

2013

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

Numerical integration of Sommerfeld integrals based on singularity extraction techniques and double exponential-type quadrature formulas

Juan Ramon Mosig, Ruzica Golubovic

A direct integration algorithm for the evaluation of Sommerfeld integrals is presented. This algorithm does not require the deformation of the integration path to avoid spectral singularities. The integration is performed along the real axis only. The algo ...

2012

Stable high-order randomized cubature formulae in arbitrary dimension

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

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

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

Infection Spread In Random Geometric Graphs

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Susceptibility of Electro-Explosive Devices to Microwave Interference

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

Numerical integration of Sommerfeld integrals based on singularity extraction techniques and double exponential-type quadrature formulas

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

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

Susceptibility of Electro-Explosive Devices to Microwave Interference

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

Infection Spread In Random Geometric Graphs

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Numerical integration of Sommerfeld integrals based on singularity extraction techniques and double exponential-type quadrature formulas

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